|
|
|
Revision difference : bibliography for axiomatics and mathematics foundations in categories |
| Version 35 |
Version 34 |
|
\subsection{Literature for axiomatic theories and
|
\subsection{Literature references for axiomatic theories and
|
| categorical foundations of mathematics} |
categorical foundations of mathematics} |
|
|
|
|
| \subsubsection{a. Foundations of mathematics, logics and |
\subsubsection{a. Foundations of mathematics, logics and |
| \PMlinkname{formal logics}{AnalyticsAndOntologyFormalLogics}: |
\PMlinkname{formal logics}{AnalyticsAndOntologyFormalLogics}: |
| axiomatics, categories, topoi and \PMlinkname{higher dimensional algebra}{HigherDimensionalAlgebraHDA}} |
axiomatics, categories, topoi and \PMlinkname{higher dimensional algebra}{HigherDimensionalAlgebraHDA}} |
|
|
| \begin{thebibliography}{99} |
\begin{thebibliography}{99} |
|
|
| \bibitem{AS96} |
\bibitem{AS96} |
| Awodey, S. 1996. ``Structure in Mathematics and Logic: A Categorical Perspective.'', {\em Philosophia Mathematica}, 3, 209--237. |
Awodey, S. 1996. ``Structure in Mathematics and Logic: A Categorical Perspective.'', {\em Philosophia Mathematica}, 3, 209--237. |
|
|
| \bibitem{AS2k6} |
\bibitem{AS2k6} |
| Awodey, S., 2006, {\em Category Theory}, Oxford: Clarendon Press. |
Awodey, S., 2006, {\em Category Theory}, Oxford: Clarendon Press. |
|
|
| \bibitem{BAJ-DJ98a} |
\bibitem{BAJ-DJ98a} |
| Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. $n$-Categories and the Algebra of Opetopes, |
Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. $n$-Categories and the Algebra of Opetopes, |
| {\em Advances in Mathematics}, 135: 145--206. |
{\em Advances in Mathematics}, 135: 145--206. |
|
|
| \bibitem{BAJ-DJ98B} |
\bibitem{BAJ-DJ98B} |
| Baez, J. and Dolan, J., 1998b, ``Categorification'', {\em Higher Category Theory, Contemporary Mathematics}, 230, Providence: AMS, 1--36. |
Baez, J. and Dolan, J., 1998b, ``Categorification'', {\em Higher Category Theory, Contemporary Mathematics}, 230, Providence: AMS, 1--36. |
|
|
| \bibitem{BBGG1} |
\bibitem{BBGG1} |
| Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and \L{}ukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., |
Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and \L{}ukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., |
| \emph{Axiomathes}, \textbf{16} Nos. 1-2: 65-122. |
\emph{Axiomathes}, \textbf{16} Nos. 1-2: 65-122. |
|
|
| \bibitem{ICBDS73} |
\bibitem{ICBDS73} |
| Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems. |
Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems. |
| \emph{Bulletin of Mathematical Biophysics}, \textbf{35}(4): 475-486. |
\emph{Bulletin of Mathematical Biophysics}, \textbf{35}(4): 475-486. |
|
|
| \bibitem{Bgg2} |
\bibitem{Bgg2} |
| Baianu, I. C., Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum Automata and N-Valued \L ukasiewicz Algebras in Relation to Dynamic Bionetworks, \textbf{(M,R)}-Systems and Their Higher Dimensional Algebra, |
Baianu, I. C., Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum Automata and N-Valued \L ukasiewicz Algebras in Relation to Dynamic Bionetworks, \textbf{(M,R)}-Systems and Their Higher Dimensional Algebra, |
| \emph{Preprint of Report}. |
\emph{Preprint of Report}. |
|
|
| \bibitem{Ba-We2k} |
\bibitem{Ba-We2k} |
| Barr, M. and C.~Wells. {\em Toposes, Triples and Theories}. Montreal: McGill University, 2000. |
Barr, M. and C.~Wells. {\em Toposes, Triples and Theories}. Montreal: McGill University, 2000. |
|
|
| \bibitem{BM-CW99} |
\bibitem{BM-CW99} |
| Barr, M. and Wells, C. 1999.\emph{Category Theory for Computing Science}, Montreal: CRM. |
Barr, M. and Wells, C. 1999.\emph{Category Theory for Computing Science}, Montreal: CRM. |
| |
|
| \bibitem{BaM98} |
\bibitem{BaM98} |
| Batanin, M. 1998. Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories., Advances in Mathematics, 136, 39--103. |
Batanin, M. 1998. Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories., Advances in Mathematics, 136, 39--103. |
|
|
| \bibitem{BJL81} |
\bibitem{BJL81} |
| Bell, J. L. 1981. Category Theory and the Foundations of Mathematics, \emph{British Journal for the Philosophy of Science}, 32, 349--358. |
Bell, J. L. 1981. Category Theory and the Foundations of Mathematics, \emph{British Journal for the Philosophy of Science}, 32, 349--358. |
| |
|
| \bibitem{BJL82} |
\bibitem{BJL82} |
| Bell, J. L., 1982. Categories, Toposes and Sets, \emph{Synthese}, 51(3): 293--337. |
Bell, J. L., 1982. Categories, Toposes and Sets, \emph{Synthese}, 51(3): 293--337. |
| |
|
| \bibitem{BA-SA83} |
\bibitem{BA-SA83} |
| Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111--140. |
Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111--140. |
|
|
| \bibitem{BA-SA89} |
\bibitem{BA-SA89} |
| Blass, A. and Scedrov, A., 1989, Freyd's Model for the Independence of the Axiom of Choice, Providence: AMS. |
Blass, A. and Scedrov, A., 1989, Freyd's Model for the Independence of the Axiom of Choice, Providence: AMS. |
|
|
| \bibitem{BASA92} |
\bibitem{BASA92} |
| Blass, A. and Scedrov, A., 1992. Complete Topoi Representing Models of Set Theory, Annals of Pure and Applied Logic , 57, no. 1, 1--26. |
Blass, A. and Scedrov, A., 1992. Complete Topoi Representing Models of Set Theory, Annals of Pure and Applied Logic , 57, no. 1, 1--26. |
|
|
| \bibitem{BA84} |
\bibitem{BA84} |
| Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5--29. |
Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5--29. |
|
|
| \bibitem{BR-SP2k4} |
\bibitem{BR-SP2k4} |
| Blute, R. and Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science |
Blute, R. and Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science |
|
|
| \bibitem{BP2k3} |
\bibitem{BP2k3} |
| Brown R. and T. Porter: 2003, Category theory and higher dimensional algebra: potential descriptive tools in neuroscience, In: {\em Proceedings of the International Conference on Theoretical Neurobiology}, Delhi, February 2003, edited by Nandini Singh, National Brain Research Centre, {\em Conference Proceedings} \textbf{1}: 80-92. |
Brown R. and T. Porter: 2003, Category theory and higher dimensional algebra: potential descriptive tools in neuroscience, In: {\em Proceedings of the International Conference on Theoretical Neurobiology}, Delhi, February 2003, edited by Nandini Singh, National Brain Research Centre, {\em Conference Proceedings} \textbf{1}: 80-92. |
|
|
| \bibitem{Br-Har-Ka-Po2k2} |
\bibitem{Br-Har-Ka-Po2k2} |
| Brown, R., Hardie, K., Kamps, H. and T. Porter: 2002, The homotopy double groupoid of a Hausdorff space., |
Brown, R., Hardie, K., Kamps, H. and T. Porter: 2002, The homotopy double groupoid of a Hausdorff space., |
| \emph{Theory and Applications of Categories} \textbf{10}, 71-93. |
\emph{Theory and Applications of Categories} \textbf{10}, 71-93. |
|
|
| \bibitem{Br-Sp76} |
\bibitem{Br-Sp76} |
| Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, \emph{Cah. Top. G\'{e}om. Diff.} \textbf{17}, 343-362. |
Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, \emph{Cah. Top. G\'{e}om. Diff.} \textbf{17}, 343-362. |
|
|
| \bibitem{BR-SCB76} |
\bibitem{BR-SCB76} |
| Brown R, Razak Salleh A (1999) Free crossed resolutions of groups and presentations of modules of |
Brown R, Razak Salleh A (1999) Free crossed resolutions of groups and presentations of modules of |
| identities among relations. {\em LMS J. Comput. Math.}, \textbf{2}: 25--61. |
identities among relations. {\em LMS J. Comput. Math.}, \textbf{2}: 25--61. |
|
|
| \bibitem{BDA55} |
\bibitem{BDA55} |
| Buchsbaum, D. A.: 1955, Exact categories and duality., {\em Trans. Amer. Math. Soc.} \textbf{80}: 1-34. |
Buchsbaum, D. A.: 1955, Exact categories and duality., {\em Trans. Amer. Math. Soc.} \textbf{80}: 1-34. |
|
|
| \bibitem{BL2k3} |
\bibitem{BL2k3} |
| Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes, \emph{Adv. in Math.} \textbf{179}, 291-317. |
Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes, \emph{Adv. in Math.} \textbf{179}, 291-317. |
|
|
| \bibitem{BM84} |
\bibitem{BM84} |
| Bunge, M., 1984, Toposes in Logic and Logic in Toposes, {\em Topoi}, 3, no. 1, 13-22. |
Bunge, M., 1984, Toposes in Logic and Logic in Toposes, {\em Topoi}, 3, no. 1, 13-22. |
|
|
| \bibitem{BM-LS2k3} |
\bibitem{BM-LS2k3} |
| Bunge M, Lack S (2003) Van Kampen theorems for toposes. {\em Adv Math}, \textbf {179}: 291-317. |
Bunge M, Lack S (2003) Van Kampen theorems for toposes. {\em Adv Math}, \textbf {179}: 291-317. |
|
|
| \bibitem{EC} |
\bibitem{EC} |
| Ehresmann, C.: 1965, \emph{Cat\'egories et Structures}, Dunod, Paris. |
Ehresmann, C.: 1965, \emph{Cat\'egories et Structures}, Dunod, Paris. |
|
|
| \bibitem{EC} |
\bibitem{EC} |
| Ehresmann, C.: 1966, Trends Toward Unity in Mathematics., \emph{Cahiers de Topologie et Geometrie Differentielle} |
Ehresmann, C.: 1966, Trends Toward Unity in Mathematics., \emph{Cahiers de Topologie et Geometrie Differentielle} |
| \textbf{8}: 1-7. |
\textbf{8}: 1-7. |
|
|
| \end{thebibliography} |
\end{thebibliography} |
|
|
|
|
| \subsubsection{b. Universal algebra, classes of algebraic structures and homology; Abelian and |
\subsubsection{b. Universal algebra, classes of algebraic structures and homology; Abelian and |
| \PMlinkname{non-Abelian theories}{NonAbelianTheories}; Algebraic |
\PMlinkname{non-Abelian theories}{NonAbelianTheories}; Algebraic |
| geometry and \PMlinkname{noncommutative geometry}{NoncommutativeGeometry}}. |
geometry and \PMlinkname{noncommutative geometry}{NoncommutativeGeometry}}. |
| |
|
| \begin{thebibliography}{199} |
\begin{thebibliography}{199} |
|
|
| \bibitem{BHR2} |
\bibitem{BHR2} |
| Brown, R., Higgins, P. J. and R. Sivera,: 2007, \emph{Non-Abelian Algebraic Topology}, |
Brown, R., Higgins, P. J. and R. Sivera,: 2007, \emph{Non-Abelian Algebraic Topology}, |
| \PMlinkexternal{vol.I pdf doc.}{http://www.bangor.ac.uk/~mas010/nonab-t/partI010604.pdf}; |
\PMlinkexternal{vol.I pdf doc.}{http://www.bangor.ac.uk/~mas010/nonab-t/partI010604.pdf}; |
| \PMlinkexternal{Review of Part I and full contents PDF doc.}{http://planetmath.org/?op=getobj&from=lec&id=75} |
\PMlinkexternal{Review of Part I and full contents PDF doc.}{http://planetmath.org/?op=getobj&from=lec&id=75} |
|
|
| \bibitem{RB2k8} |
\bibitem{RB2k8} |
| R. Brown. 2008. {\em Higher Dimensional Algebra Preprint as pdf and ps docs. at arXiv:math/0212274v6 [math.AT]} |
R. Brown. 2008. {\em Higher Dimensional Algebra Preprint as pdf and ps docs. at arXiv:math/0212274v6 [math.AT]} |
|
|
| \bibitem{Br-Hardy76} |
\bibitem{Br-Hardy76} |
| Brown, R., and Hardy, J.P.L.:1976, Topological groupoids I: universal constructions, \emph{Math. Nachr.}, \textbf{71}: 273-286. |
Brown, R., and Hardy, J.P.L.:1976, Topological groupoids I: universal constructions, \emph{Math. Nachr.}, \textbf{71}: 273-286. |
|
|
| \bibitem{CH-ES56} |
\bibitem{CH-ES56} |
| Cartan, H. and Eilenberg, S. 1956. {\em Homological Algebra}, Princeton Univ. Press: Pinceton. |
Cartan, H. and Eilenberg, S. 1956. {\em Homological Algebra}, Princeton Univ. Press: Pinceton. |
|
|
| \bibitem{CC46} |
\bibitem{CC46} |
| Chevalley, C. 1946. The theory of Lie groups. Princeton University Press, Princeton NJ. |
Chevalley, C. 1946. The theory of Lie groups. Princeton University Press, Princeton NJ. |
|
|
| \bibitem{Chaician} |
\bibitem{Chaician} |
| M. Chaician and A. Demichev. 1996. Introduction to Quantum Groups, World Scientific . |
M. Chaician and A. Demichev. 1996. Introduction to Quantum Groups, World Scientific . |
|
|
| \bibitem{CPM65} |
\bibitem{CPM65} |
| Cohen, P.M. 1965. {\em Universal Algebra}, Harper and Row: New York, London and Tokyo. |
Cohen, P.M. 1965. {\em Universal Algebra}, Harper and Row: New York, London and Tokyo. |
|
|
| \bibitem{CA94} |
\bibitem{CA94} |
| Connes A 1994. \emph{Noncommutative geometry}. Academic Press: New York. |
Connes A 1994. \emph{Noncommutative geometry}. Academic Press: New York. |
|
|
| \bibitem{CR-LL63} |
\bibitem{CR-LL63} |
| Croisot, R. and Lesieur, L. 1963. \emph{Alg\`ebre noeth\'erienne non-commutative.}, |
Croisot, R. and Lesieur, L. 1963. \emph{Alg\`ebre noeth\'erienne non-commutative.}, |
| Gauthier-Villard: Paris. |
Gauthier-Villard: Paris. |
|
|
| \bibitem{CRL94} |
\bibitem{CRL94} |
| Crole, R.L., 1994, {\em Categories for Types}, Cambridge: Cambridge University Press. |
Crole, R.L., 1994, {\em Categories for Types}, Cambridge: Cambridge University Press. |
|
|
| \bibitem{DJ-ALEX60-71} |
\bibitem{DJ-ALEX60-71} |
| Dieudonn\'e, J. and Grothendieck, A., 1960, [1971], {\em \'El\'ements de G\'eom\'etrie Alg\'ebrique}, Berlin: Springer-Verlag. |
Dieudonn\'e, J. and Grothendieck, A., 1960, [1971], {\em \'El\'ements de G\'eom\'etrie Alg\'ebrique}, Berlin: Springer-Verlag. |
|
|
| \bibitem{Dixmier} |
\bibitem{Dixmier} |
| Dixmier, J., 1981, Von Neumann Algebras, Amsterdam: North-Holland Publishing Company. [First published in French in 1957: Les Algebres d'Operateurs dans l'Espace Hilbertien, Paris: Gauthier--Villars.] |
Dixmier, J., 1981, Von Neumann Algebras, Amsterdam: North-Holland Publishing Company. [First published in French in 1957: Les Algebres d'Operateurs dans l'Espace Hilbertien, Paris: Gauthier--Villars.] |
|
|
| \bibitem{Durdevich1} |
\bibitem{Durdevich1} |
| M. Durdevich : Geometry of quantum principal bundles I, Commun. Math. Phys. \textbf{175} (3) (1996), 457--521. |
M. Durdevich : Geometry of quantum principal bundles I, Commun. Math. Phys. \textbf{175} (3) (1996), 457--521. |
|
|
| \bibitem{Durdevich2} |
\bibitem{Durdevich2} |
| M. Durdevich : Geometry of quantum principal bundles II, Rev.Math. Phys. \textbf{9} (5) (1997), 531-607. |
M. Durdevich : Geometry of quantum principal bundles II, Rev.Math. Phys. \textbf{9} (5) (1997), 531-607. |
|
|
| \bibitem{Eh-pseudo} |
\bibitem{Eh-pseudo} |
| Ehresmann, C.: 1952, Structures locales et structures infinit\'esimales, \emph{C.R.A.S.} Paris \textbf{274}: 587-589. |
Ehresmann, C.: 1952, Structures locales et structures infinit\'esimales, \emph{C.R.A.S.} Paris \textbf{274}: 587-589. |
|
|
| \bibitem{Eh} |
\bibitem{Eh} |
| Ehresmann, C.: 1959, Cat\'egories topologiques et cat\'egories diff\'erentiables, \emph{Coll. G\'eom. Diff. Glob.} Bruxelles, pp.137-150. |
Ehresmann, C.: 1959, Cat\'egories topologiques et cat\'egories diff\'erentiables, \emph{Coll. G\'eom. Diff. Glob.} Bruxelles, pp.137-150. |
|
|
| \bibitem{Eh-quintettes} |
\bibitem{Eh-quintettes} |
| Ehresmann, C.:1963, Cat\'egories doubles des quintettes: applications covariantes , \emph{C.R.A.S. Paris}, \textbf{256}: 1891--1894. |
Ehresmann, C.:1963, Cat\'egories doubles des quintettes: applications covariantes , \emph{C.R.A.S. Paris}, \textbf{256}: 1891--1894. |
|
|
| \bibitem{Eh-Oe} |
\bibitem{Eh-Oe} |
| Ehresmann, C.: 1984, \emph{Oeuvres compl\`etes et comment\'ees: Amiens, 1980-84}, edited and commented by Andr\'ee Ehresmann. |
Ehresmann, C.: 1984, \emph{Oeuvres compl\`etes et comment\'ees: Amiens, 1980-84}, edited and commented by Andr\'ee Ehresmann. |
|
|
| \bibitem{EML1} |
\bibitem{EML1} |
| Eilenberg, S. and S. Mac Lane.: 1942, Natural Isomorphisms in Group Theory., \emph{American Mathematical Society 43}: 757-831. |
Eilenberg, S. and S. Mac Lane.: 1942, Natural Isomorphisms in Group Theory., \emph{American Mathematical Society 43}: 757-831. |
|
|
| \bibitem{EL} |
\bibitem{EL} |
| Eilenberg, S. and S. Mac Lane: 1945, The General Theory of Natural Equivalences, \emph{Transactions of the American Mathematical Society} \textbf{58}: 231-294. |
Eilenberg, S. and S. Mac Lane: 1945, The General Theory of Natural Equivalences, \emph{Transactions of the American Mathematical Society} \textbf{58}: 231-294. |
|
|
| \bibitem{ES-CH56} |
\bibitem{ES-CH56} |
| Eilenberg, S. \& Cartan, H., 1956, {\em Homological Algebra}, Princeton: Princeton University Press. |
Eilenberg, S. \& Cartan, H., 1956, {\em Homological Algebra}, Princeton: Princeton University Press. |
|
|
| \bibitem{ES-MCLS42} |
\bibitem{ES-MCLS42} |
| Eilenberg, S. \& MacLane, S., 1942, Group Extensions and Homology, {\em Annals of Mathematics}, 43, 757--831. |
Eilenberg, S. \& MacLane, S., 1942, Group Extensions and Homology, {\em Annals of Mathematics}, 43, 757--831. |
|
|
| \bibitem{ES-SN52} |
\bibitem{ES-SN52} |
| Eilenberg, S. \& Steenrod, N., 1952, {\em Foundations of Algebraic Topology}, Princeton: Princeton University Press. |
Eilenberg, S. \& Steenrod, N., 1952, {\em Foundations of Algebraic Topology}, Princeton: Princeton University Press. |
|
|
| \bibitem{ES60} |
\bibitem{ES60} |
| Eilenberg, S.: 1960. Abstract description of some basic functors., J. Indian Math.Soc., \textbf{24} :221-234. |
Eilenberg, S.: 1960. Abstract description of some basic functors., J. Indian Math.Soc., \textbf{24} :221-234. |
|
|
| \bibitem{S.Eilenberg} |
\bibitem{S.Eilenberg} |
| S.Eilenberg. Relations between Homology and Homotopy Groups. {\em Proc.Natl.Acad.Sci.USA} (1966),v:10--14. |
S.Eilenberg. Relations between Homology and Homotopy Groups. {\em Proc.Natl.Acad.Sci.USA} (1966),v:10--14. |
|
|
| \bibitem{ED88} |
\bibitem{ED88} |
| Ellerman, D., 1988, Category Theory and Concrete Universals, {\em Synthese}, 28, 409--429. |
Ellerman, D., 1988, Category Theory and Concrete Universals, {\em Synthese}, 28, 409--429. |
|
|
| \bibitem{ETH} |
\bibitem{ETH} |
| Ezawa,Z.F., G. Tsitsishvilli and K. Hasebe : Noncommutative geometry, extended $W_{\infty}$ algebra and Grassmannian solitons in multicomponent Hall systems, (at arXiv:hep--th/0209198). |
Ezawa,Z.F., G. Tsitsishvilli and K. Hasebe : Noncommutative geometry, extended $W_{\infty}$ algebra and Grassmannian solitons in multicomponent Hall systems, (at arXiv:hep--th/0209198). |
|
|
| \bibitem{FP2k2} |
\bibitem{FP2k2} |
| Freyd, P., 2002, Cartesian Logic, {\em Theoretical Computer Science}, 278, no. 1--2, 3--21. |
Freyd, P., 2002, Cartesian Logic, {\em Theoretical Computer Science}, 278, no. 1--2, 3--21. |
|
|
| \bibitem{FP-FH-SA87} |
\bibitem{FP-FH-SA87} |
| Freyd, P., Friedman, H. \& Scedrov, A., 1987, Lindembaum Algebras of Intuitionistic Theories and Free Categories, {\em Annals of Pure and Applied Logic}, 35, 2, 167--172. |
Freyd, P., Friedman, H. \& Scedrov, A., 1987, Lindembaum Algebras of Intuitionistic Theories and Free Categories, {\em Annals of Pure and Applied Logic}, 35, 2, 167--172. |
|
|
| \bibitem{Gablot} |
\bibitem{Gablot} |
| Gablot, R. 1971. Sur deux classes de cat\'{e}gories de Grothendieck. {\em Thesis}, Univ. de Lille. |
Gablot, R. 1971. Sur deux classes de cat\'{e}gories de Grothendieck. {\em Thesis}, Univ. de Lille. |
|
|
| \bibitem{Gabriel1} |
\bibitem{Gabriel1} |
| Gabriel, P.: 1962, Des cat\'egories ab\'eliennes, \emph{Bull. Soc. Math. France} \textbf{90}: 323-448. |
Gabriel, P.: 1962, Des cat\'egories ab\'eliennes, \emph{Bull. Soc. Math. France} \textbf{90}: 323-448. |
|
|
| \bibitem{Gabriel2} |
\bibitem{Gabriel2} |
| Gabriel, P. and M.Zisman:. 1967: \emph{Category of fractions and homotopy theory}, \emph{Ergebnesse der math.} Springer: Berlin. |
Gabriel, P. and M.Zisman:. 1967: \emph{Category of fractions and homotopy theory}, \emph{Ergebnesse der math.} Springer: Berlin. |
|
|
| \bibitem{GabrielNP} |
\bibitem{GabrielNP} |
| Gabriel, P. and N. Popescu: 1964, Caract\'{e}risation des cat\'egories ab\'eliennes |
Gabriel, P. and N. Popescu: 1964, Caract\'{e}risation des cat\'egories ab\'eliennes |
| avec g\'{e}n\'{e}rateurs et limites inductives. , \emph{CRAS Paris} \textbf{258}: 4188-4191. |
avec g\'{e}n\'{e}rateurs et limites inductives. , \emph{CRAS Paris} \textbf{258}: 4188-4191. |
|
|
| \bibitem{GA-RG-SM2k} |
\bibitem{GA-RG-SM2k} |
| Galli, A. \& Reyes, G. \& Sagastume, M., 2000, Completeness Theorems via the Double Dual Functor, |
Galli, A. \& Reyes, G. \& Sagastume, M., 2000, Completeness Theorems via the Double Dual Functor, |
| {\em Studia Logica}, \textbf{64}, no. 1: 61--81. |
{\em Studia Logica}, \textbf{64}, no. 1: 61--81. |
|
|
| \bibitem{GN} |
\bibitem{GN} |
| Gelfan'd, I. and Naimark, M., 1943, On the Imbedding of Normed Rings into the Ring of Operators in Hilbert Space, Recueil Math\'ematique [Matematicheskii Sbornik] Nouvelle S\'erie, 12 [54]: 197--213. [Reprinted in C*--algebras: |
Gelfan'd, I. and Naimark, M., 1943, On the Imbedding of Normed Rings into the Ring of Operators in Hilbert Space, Recueil Math\'ematique [Matematicheskii Sbornik] Nouvelle S\'erie, 12 [54]: 197--213. [Reprinted in C*--algebras: |
| 1943--1993, in the series Contemporary Mathematics, 167, Providence, R.I.: American Mathematical Society, 1994.] |
1943--1993, in the series Contemporary Mathematics, 167, Providence, R.I.: American Mathematical Society, 1994.] |
|
|
| \bibitem{GS-ZM2K2} |
\bibitem{GS-ZM2K2} |
| Ghilardi, S. \& Zawadowski, M., 2002, {\em Sheaves, Games \& Model Completions: A Categorical Approach to Nonclassical Propositional Logics}, Dordrecht: Kluwer. |
Ghilardi, S. \& Zawadowski, M., 2002, {\em Sheaves, Games \& Model Completions: A Categorical Approach to Nonclassical Propositional Logics}, Dordrecht: Kluwer. |
|
|
| \bibitem{gs89} |
\bibitem{gs89} |
| Ghilardi, S., 1989, Presheaf Semantics and Independence Results for some Non-classical first-order logics, |
Ghilardi, S., 1989, Presheaf Semantics and Independence Results for some Non-classical first-order logics, |
| {\em Archive for Mathematical Logic}, 29, no. 2, 125--136. |
{\em Archive for Mathematical Logic}, 29, no. 2, 125--136. |
|
|
| \bibitem{Gob68} |
\bibitem{Gob68} |
| Goblot, R., 1968, Cat\'egories modulaires , {\em C. R. Acad. Sci. Paris, S\'erie A.}, \textbf{267}: 381--383. |
Goblot, R., 1968, Cat\'egories modulaires , {\em C. R. Acad. Sci. Paris, S\'erie A.}, \textbf{267}: 381--383. |
|
|
| \bibitem{Gob71} |
\bibitem{Gob71} |
| Goblot, R., 1971, Sur deux classes de cat\'egories de Grothendieck, {\em Th\`ese.}, Univ. Lille, 1971. |
Goblot, R., 1971, Sur deux classes de cat\'egories de Grothendieck, {\em Th\`ese.}, Univ. Lille, 1971. |
|
|
| \bibitem{GR79} |
\bibitem{GR79} |
| Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and the foundations of mathematics, Amsterdam: Elsevier North-Holland Publ. Comp. |
Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and the foundations of mathematics, Amsterdam: Elsevier North-Holland Publ. Comp. |
|
|
| \bibitem{Goldie} |
\bibitem{Goldie} |
| Goldie, A. W., 1964, Localization in non-commutative noetherian rings, {\em J.Algebra}, \textbf{1}: 286-297. |
Goldie, A. W., 1964, Localization in non-commutative noetherian rings, {\em J.Algebra}, \textbf{1}: 286-297. |
|
|
| \bibitem{Godement} |
\bibitem{Godement} |
| Godement,R. 1958. Th\'{e}orie des faisceaux. Hermann: Paris. |
Godement,R. 1958. Th\'{e}orie des faisceaux. Hermann: Paris. |
|
|
| \bibitem{GRAY65} |
\bibitem{GRAY65} |
| Gray, C. W.: 1965. Sheaves with values in a category.,\emph {Topology}, 3: 1-18. |
Gray, C. W.: 1965. Sheaves with values in a category.,\emph {Topology}, 3: 1-18. |
|
|
| \bibitem{Alex71} |
\bibitem{Alex71} |
| Grothendieck, A.: 1971, Rev\^{e}tements \'Etales et Groupe Fondamental (SGA1), |
Grothendieck, A.: 1971, Rev\^{e}tements \'Etales et Groupe Fondamental (SGA1), |
| chapter VI: Cat\'egories fibr\'ees et descente, \emph{Lecture Notes in Math.} |
chapter VI: Cat\'egories fibr\'ees et descente, \emph{Lecture Notes in Math.} |
| \textbf{224}, Springer--Verlag: Berlin. |
\textbf{224}, Springer--Verlag: Berlin. |
|
|
| \bibitem{Alex57} |
\bibitem{Alex57} |
| Grothendieck, A.: 1957, Sur quelque point d-alg\`{e}bre homologique. , \emph{Tohoku Math. J.}, \textbf{9:} 119-121. |
Grothendieck, A.: 1957, Sur quelque point d-alg\`{e}bre homologique. , \emph{Tohoku Math. J.}, \textbf{9:} 119-121. |
|
|
| \bibitem{Alex3} |
\bibitem{Alex3} |
| Grothendieck, A. and J. Dieudon\'{e}.: 1960, El\'{e}ments de geometrie alg\'{e}brique., \emph{Publ. Inst. des Hautes Etudes de Science}, \textbf{4}. |
Grothendieck, A. and J. Dieudon\'{e}.: 1960, El\'{e}ments de geometrie alg\'{e}brique., \emph{Publ. Inst. des Hautes Etudes de Science}, \textbf{4}. |
|
|
| \bibitem{ALEXsem} |
\bibitem{ALEXsem} |
| Grothendieck, A. et al., S\'eminaire de G\'eom\'etrie Alg\'ebrique, Vol. 1--7, Berlin: Springer-Verlag. |
Grothendieck, A. et al., S\'eminaire de G\'eom\'etrie Alg\'ebrique, Vol. 1--7, Berlin: Springer-Verlag. |
|
|
| \bibitem{HKK} |
\bibitem{HKK} |
| Hardie, K.A. K.H. Kamps and R.W. Kieboom, A homotopy 2-groupoid of a Hausdorff space, {\em Applied Cat. Structures} 8 (2000), 209-234. |
Hardie, K.A. K.H. Kamps and R.W. Kieboom, A homotopy 2-groupoid of a Hausdorff space, {\em Applied Cat. Structures} 8 (2000), 209-234. |
|
|
| \bibitem{HWS82} |
\bibitem{HWS82} |
| Hatcher, W. S., 1982, {\em The Logical Foundations of Mathematics}, Oxford: Pergamon Press. |
Hatcher, W. S., 1982, {\em The Logical Foundations of Mathematics}, Oxford: Pergamon Press. |
| |
|
| \bibitem{Heller58} |
\bibitem{Heller58} |
| Heller, A. :1958, Homological algebra in Abelian categories., \emph{Ann. of Math.} |
Heller, A. :1958, Homological algebra in Abelian categories., \emph{Ann. of Math.} |
| \textbf{68}: 484-525. |
\textbf{68}: 484-525. |
|
|
| \bibitem{HellerRowe62} |
\bibitem{HellerRowe62} |
| Heller, A. and K. A. Rowe.:1962, On the category of sheaves., \emph{Amer J. Math.} |
Heller, A. and K. A. Rowe.:1962, On the category of sheaves., \emph{Amer J. Math.} |
| \textbf{84}: 205-216. |
\textbf{84}: 205-216. |
|
|
| \bibitem{HG2k3} |
\bibitem{HG2k3} |
| Hellman, G., 2003, "Does Category Theory Provide a Framework for Mathematical Structuralism?", Philosophia Mathematica, 11, 2, 129--157. |
Hellman, G., 2003, "Does Category Theory Provide a Framework for Mathematical Structuralism?", Philosophia Mathematica, 11, 2, 129--157. |
|
|
| \bibitem{HC-MM-PJ2K} |
\bibitem{HC-MM-PJ2K} |
| Hermida, C. \& Makkai, M. \& Power, J., 2000, On Weak Higher-dimensional Categories I, Journal of Pure and Applied Algebra, 154, no. 1-3, 221--246. |
Hermida, C. \& Makkai, M. \& Power, J., 2000, On Weak Higher-dimensional Categories I, Journal of Pure and Applied Algebra, 154, no. 1-3, 221--246. |
|
|
| \bibitem{HC-MM-PI2K1} |
\bibitem{HC-MM-PI2K1} |
| Hermida, C. \& Makkai, M. \& Power, J., 2001, On Weak Higher-dimensional Categories II, Journal of Pure and Applied Algebra, 157, no. 2-3, 247--277. |
Hermida, C. \& Makkai, M. \& Power, J., 2001, On Weak Higher-dimensional Categories II, Journal of Pure and Applied Algebra, 157, no. 2-3, 247--277. |
|
|
| \bibitem{HC-MM-PI2K2} |
\bibitem{HC-MM-PI2K2} |
| Hermida, C. \& Makkai, M. \& Power, J., 2002, On Weak Higher-dimensional Categories III, Journal of Pure and Applied Algebra, 166, no. 1-2, 83--104. |
Hermida, C. \& Makkai, M. \& Power, J., 2002, On Weak Higher-dimensional Categories III, Journal of Pure and Applied Algebra, 166, no. 1-2, 83--104. |
|
|
| \bibitem{HPJbook} |
\bibitem{HPJbook} |
| Higgins, P. J.: 2005, \emph{Categories and groupoids}, Van Nostrand Mathematical Studies: 32, (1971); \emph{Reprints in |
Higgins, P. J.: 2005, \emph{Categories and groupoids}, Van Nostrand Mathematical Studies: 32, (1971); \emph{Reprints in |
| Theory and Applications of Categories}, No. 7: 1-195. |
Theory and Applications of Categories}, No. 7: 1-195. |
|
|
| \bibitem{HPJ2k5} |
\bibitem{HPJ2k5} |
| Higgins, Philip J. Thin elements and commutative shells in cubical $\omega$-categories. Theory Appl. Categ. 14 (2005), No. 4, 60--74 (electronic). msc: 18D05. |
Higgins, Philip J. Thin elements and commutative shells in cubical $\omega$-categories. Theory Appl. Categ. 14 (2005), No. 4, 60--74 (electronic). msc: 18D05. |
|
|
| \bibitem{HJ-RE-RG90} |
\bibitem{HJ-RE-RG90} |
| Hyland, J.M.E. \& Robinson, E.P. \& Rosolini, G., 1990, The Discrete Objects in the Effective Topos, |
Hyland, J.M.E. \& Robinson, E.P. \& Rosolini, G., 1990, The Discrete Objects in the Effective Topos, |
| {\em Proceedings of the London Mathematical Society} (3), 60, no. 1, 1--36. |
{\em Proceedings of the London Mathematical Society} (3), 60, no. 1, 1--36. |
|
|
| \bibitem{HJME82} |
\bibitem{HJME82} |
| Hyland, J.M.E., 1982, The Effective Topos, {\em Studies in Logic and the Foundations of Mathematics}, 110, Amsterdam: North Holland, 165--216. |
Hyland, J.M.E., 1982, The Effective Topos, {\em Studies in Logic and the Foundations of Mathematics}, 110, Amsterdam: North Holland, 165--216. |
|
|
| \bibitem{HJME88} |
\bibitem{HJME88} |
| Hyland, J. M..E., 1988, A Small Complete Category, {\em Annals of Pure and Applied Logic}, 40, no. 2, 135--165. |
Hyland, J. M..E., 1988, A Small Complete Category, {\em Annals of Pure and Applied Logic}, 40, no. 2, 135--165. |
|
|
| \bibitem{HJME91} |
\bibitem{HJME91} |
| Hyland, J. M .E., 1991, First Steps in Synthetic Domain Theory, {\em Category Theory (Como 1990)}, Lecture Notes in Mathematics, 1488, Berlin: Springer, 131-156. |
Hyland, J. M .E., 1991, First Steps in Synthetic Domain Theory, {\em Category Theory (Como 1990)}, Lecture Notes in Mathematics, 1488, Berlin: Springer, 131-156. |
|
|
| \bibitem{HJME2K2} |
\bibitem{HJME2K2} |
| Hyland, J. M.E., 2002, Proof Theory in the Abstract, {\em Annals of Pure and Applied Logic}, 114, no. 1--3, 43--78. |
Hyland, J. M.E., 2002, Proof Theory in the Abstract, {\em Annals of Pure and Applied Logic}, 114, no. 1--3, 43--78. |
|
|
| \bibitem{E.Hurewicz} |
\bibitem{E.Hurewicz} |
| E.Hurewicz. CW Complexes., {\em Trans AMS}.1955. |
E.Hurewicz. CW Complexes., {\em Trans AMS}.1955. |
|
|
| \bibitem{JB99} |
\bibitem{JB99} |
| Jacobs, B., 1999, Categorical Logic and Type Theory, Amsterdam: North Holland. |
Jacobs, B., 1999, Categorical Logic and Type Theory, Amsterdam: North Holland. |
|
|
| \bibitem{JPT77} |
\bibitem{JPT77} |
| Johnstone, P. T., 1977, Topos Theory, New York: Academic Press. |
Johnstone, P. T., 1977, Topos Theory, New York: Academic Press. |
|
|
| \bibitem{JPT79A} |
\bibitem{JPT79A} |
| Johnstone, P. T., 1979a, {\em Conditions Related to De Morgan's Law, Applications of Sheaves}, Lecture Notes in Mathematics, 753, Berlin: Springer, 479--491. |
Johnstone, P. T., 1979a, {\em Conditions Related to De Morgan's Law, Applications of Sheaves}, Lecture Notes in Mathematics, 753, Berlin: Springer, 479--491. |
|
|
| \bibitem{JPT81} |
\bibitem{JPT81} |
| Johnstone, P. T., 1981, Tychonoff's Theorem without the Axiom of Choice, |
Johnstone, P. T., 1981, Tychonoff's Theorem without the Axiom of Choice, |
| {\em Fundamenta Mathematicae}, 113, no. 1, 21--35. |
{\em Fundamenta Mathematicae}, 113, no. 1, 21--35. |
|
|
| \bibitem{JPT52} |
\bibitem{JPT52} |
| Johnstone, P. T., 1982, {\em Stone Spaces}, Cambridge:Cambridge University Press. |
Johnstone, P. T., 1982, {\em Stone Spaces}, Cambridge:Cambridge University Press. |
|
|
| \bibitem{JPT85} |
\bibitem{JPT85} |
| Johnstone, P. T., 1985, How General is a Generalized Space?, {\em Aspects of Topology}, Cambridge: Cambridge University Press, 77--111. |
Johnstone, P. T., 1985, How General is a Generalized Space?, {\em Aspects of Topology}, Cambridge: Cambridge University Press, 77--111. |
|
|
| \bibitem{JAMI95} |
\bibitem{JAMI95} |
| Joyal, A. \& Moerdijk, I., 1995, {\em Algebraic Set Theory}, Cambridge: Cambridge University Press. |
Joyal, A. \& Moerdijk, I., 1995, {\em Algebraic Set Theory}, Cambridge: Cambridge University Press. |
|
|
| \bibitem{kampen1-1933} |
\bibitem{kampen1-1933} |
| Van Kampen, E. H.: 1933, On the Connection Between the Fundamental |
Van Kampen, E. H.: 1933, On the Connection Between the Fundamental |
| Groups of some Related Spaces, \emph{Amer. J. Math.} \textbf{55}: 261-267 |
Groups of some Related Spaces, \emph{Amer. J. Math.} \textbf{55}: 261-267 |
|
|
| \bibitem{KDM58} |
\bibitem{KDM58} |
| Kan, D. M., 1958, Adjoint Functors, {\em Transactions of the American Mathematical Society} 87, 294-329. |
Kan, D. M., 1958, Adjoint Functors, {\em Transactions of the American Mathematical Society} 87, 294-329. |
|
|
| \bibitem{Kleisli62} |
\bibitem{Kleisli62} |
| Kleisli, H.: 1962, Homotopy theory in Abelian categories.,{\em Can. J. Math.}, \textbf{14}: 139-169. |
Kleisli, H.: 1962, Homotopy theory in Abelian categories.,{\em Can. J. Math.}, \textbf{14}: 139-169. |
|
|
| \bibitem{KJT70} |
\bibitem{KJT70} |
| Knight, J.T., 1970, On epimorphisms of non-commutative rings., {\em Proc. Cambridge Phil. Soc.}, |
Knight, J.T., 1970, On epimorphisms of non-commutative rings., {\em Proc. Cambridge Phil. Soc.}, |
| \textbf{25}: 266-271. |
\textbf{25}: 266-271. |
|
|
| \bibitem{KA81} |
\bibitem{KA81} |
| Kock, A., 1981, {\em Synthetic Differential Geometry}, London Mathematical Society Lecture Note Series, 51, Cambridge: Cambridge University Press. |
Kock, A., 1981, {\em Synthetic Differential Geometry}, London Mathematical Society Lecture Note Series, 51, Cambridge: Cambridge University Press. |
|
|
| \bibitem{KN1} |
\bibitem{KN1} |
| S. Kobayashi and K. Nomizu : {\em Foundations of Differential Geometry}, Vol I., Wiley Interscience, New York--London 1963. |
S. Kobayashi and K. Nomizu : {\em Foundations of Differential Geometry}, Vol I., Wiley Interscience, New York--London 1963. |
|
|
| \bibitem{Krips} |
\bibitem{Krips} |
| H. Krips : Measurement in Quantum Theory, \emph{The Stanford Encyclopedia of Philosophy } (Winter 1999 Edition), |
H. Krips : Measurement in Quantum Theory, \emph{The Stanford Encyclopedia of Philosophy } (Winter 1999 Edition), |
| Edward N. Zalta (ed.), |
Edward N. Zalta (ed.), |
|
|
| \bibitem{LTY} |
\bibitem{LTY} |
| Lam, T. Y., 1966, The category of noetherian modules, {\em Proc. Natl. Acad. Sci. USA}, \textbf{55}: 1038-104. |
Lam, T. Y., 1966, The category of noetherian modules, {\em Proc. Natl. Acad. Sci. USA}, \textbf{55}: 1038-104. |
|
|
| \bibitem{LJ-SPJ86} |
\bibitem{LJ-SPJ86} |
| Lambek, J. \& Scott, P.J., 1986, {\em Introduction to Higher Order Categorical Logic}, Cambridge: Cambridge University Press. |
Lambek, J. \& Scott, P.J., 1986, {\em Introduction to Higher Order Categorical Logic}, Cambridge: Cambridge University Press. |
|
|
| \bibitem{LJ68} |
\bibitem{LJ68} |
| Lambek, J., 1968, Deductive Systems and Categories I. Syntactic Calculus and Residuated Categories, |
Lambek, J., 1968, Deductive Systems and Categories I. Syntactic Calculus and Residuated Categories, |
| {\em Mathematical Systems Theory}, 2, 287--318. |
{\em Mathematical Systems Theory}, 2, 287--318. |
|
|
| \bibitem{LJ69} |
\bibitem{LJ69} |
| Lambek, J., 1969, {\em Deductive Systems and Categories II. Standard Constructions and Closed Categories, Category Theory, Homology Theory and their Applications I}, Berlin: Springer, 76--122. |
Lambek, J., 1969, {\em Deductive Systems and Categories II. Standard Constructions and Closed Categories, Category Theory, Homology Theory and their Applications I}, Berlin: Springer, 76--122. |
|
|
| \bibitem{LJ72} |
\bibitem{LJ72} |
| Lambek, J., 1972, {\em Deductive Systems and Categories III. Cartesian Closed Categories, Intuitionistic Propositional Calculus, and Combinatory Logic, Toposes, Algebraic Geometry and Logic}, Lecture Notes in Mathematics, 274, Berlin: Springer, 57--82. |
Lambek, J., 1972, {\em Deductive Systems and Categories III. Cartesian Closed Categories, Intuitionistic Propositional Calculus, and Combinatory Logic, Toposes, Algebraic Geometry and Logic}, Lecture Notes in Mathematics, 274, Berlin: Springer, 57--82. |
|
|
| \bibitem{LT89A} |
\bibitem{LT89A} |
| Lambek, J., 1989A, On Some Connections Between Logic and Category Theory, {\em Studia Logica}, 48, 3, 269--278. |
Lambek, J., 1989A, On Some Connections Between Logic and Category Theory, {\em Studia Logica}, 48, 3, 269--278. |
|
|
| \bibitem{LJ89B} |
\bibitem{LJ89B} |
| Lambek, J., 1989B, On the Sheaf of Possible Worlds, {\em Categorical Topology and its relation to Analysis, Algebra and Combinatorics}, Teaneck: World Scientific Publishing, 36--53. |
Lambek, J., 1989B, On the Sheaf of Possible Worlds, {\em Categorical Topology and its relation to Analysis, Algebra and Combinatorics}, Teaneck: World Scientific Publishing, 36--53. |
|
|
| \bibitem{LJ94a} |
\bibitem{LJ94a} |
| Lambek, J., 1994a, Some Aspects of Categorical Logic, in {\em Logic, Methodology and Philosophy of Science IX, Studies in Logic and the Foundations of Mathematics} \textbf{134}, Amsterdam: North Holland, 69--89. |
Lambek, J., 1994a, Some Aspects of Categorical Logic, in {\em Logic, Methodology and Philosophy of Science IX, Studies in Logic and the Foundations of Mathematics} \textbf{134}, Amsterdam: North Holland, 69--89. |
| |
|
| \bibitem{LJ2k4} |
\bibitem{LJ2k4} |
| Lambek, J., 2004, What is the world of Mathematics? Provinces of Logic Determined, {\em Annals of Pure and Applied Logic}, \textbf{126}(1-3), 149--158. |
Lambek, J., 2004, What is the world of Mathematics? Provinces of Logic Determined, {\em Annals of Pure and Applied Logic}, \textbf{126}(1-3), 149--158. |
|
|
| \bibitem{LaSc} |
\bibitem{LaSc} |
| Lambek, J. and P.~J.~Scott. {\em Introduction to higher order categorical logic}. Cambridge University Press, 1986. |
Lambek, J. and P.~J.~Scott. {\em Introduction to higher order categorical logic}. Cambridge University Press, 1986. |
|
|
| \bibitem{Lance} |
\bibitem{Lance} |
| E. C. Lance: Hilbert C*--Modules. \emph{London Math. Soc. Lect. Notes} \textbf{210}, \emph{Cambridge Univ. Press.} 1995. |
E. C. Lance: Hilbert C*--Modules. \emph{London Math. Soc. Lect. Notes} \textbf{210}, \emph{Cambridge Univ. Press.} 1995. |
|
|
| \bibitem{LE-MJP2k5} |
\bibitem{LE-MJP2k5} |
| Landry, E. \& Marquis, J.-P., 2005, Categories in Context: Historical, Foundational and philosophical, |
Landry, E. \& Marquis, J.-P., 2005, Categories in Context: Historical, Foundational and philosophical, |
| {\em Philosophia Mathematica}, 13, 1--43. |
{\em Philosophia Mathematica}, 13, 1--43. |
|
|
| \bibitem{LE99} |
\bibitem{LE99} |
| Landry, E., 1999, Category Theory: the Language of Mathematics, {\em Philosophy of Science}, 66, 3: supplement, S14--S27. |
Landry, E., 1999, Category Theory: the Language of Mathematics, {\em Philosophy of Science}, 66, 3: supplement, S14--S27. |
|
|
| \bibitem{LandNP98} |
\bibitem{LandNP98} |
| Landsman, N. P.: 1998, \emph{Mathematical Topics between Classical and Quantum Mechanics}, Springer Verlag: New York. |
Landsman, N. P.: 1998, \emph{Mathematical Topics between Classical and Quantum Mechanics}, Springer Verlag: New York. |
|
|
| \bibitem{Land1} |
\bibitem{Land1} |
| Landsman, N. P. : Compact quantum groupoids, (at arXiv:math--ph/9912006). |
Landsman, N. P. : Compact quantum groupoids, (at arXiv:math--ph/9912006). |
|
|
| \bibitem{LPRM94} |
\bibitem{LPRM94} |
| La Palme Reyes, M., et. al., 1994, The non-Boolean Logic of Natural Language Negation, |
La Palme Reyes, M., et. al., 1994, The non-Boolean Logic of Natural Language Negation, |
| {\em Philosophia Mathematica}, \textbf{2}, no. 1, 45--68. |
{\em Philosophia Mathematica}, \textbf{2}, no. 1, 45--68. |
|
|
| \bibitem{LPRM99} |
\bibitem{LPRM99} |
| La Palme Reyes, M., et. al., 1999, {\em Count Nouns, Mass Nouns, and their Transformations: a Unified Category-theoretic Semantics, Language, Logic and Concepts}, Cambridge: MIT Press, 427--452. |
La Palme Reyes, M., et. al., 1999, {\em Count Nouns, Mass Nouns, and their Transformations: a Unified Category-theoretic Semantics, Language, Logic and Concepts}, Cambridge: MIT Press, 427--452. |
| |
|
| \bibitem{LFW64} |
\bibitem{LFW64} |
| Lawvere, F. W., 1964, An Elementary Theory of the Category of Sets, {\em Proceedings of the National Academy of Sciences U.S.A.}, 52, 1506--1511. |
Lawvere, F. W., 1964, An Elementary Theory of the Category of Sets, {\em Proceedings of the National Academy of Sciences U.S.A.}, 52, 1506--1511. |
|
|
| \bibitem{LFW65} |
\bibitem{LFW65} |
| Lawvere, F. W., 1965, Algebraic Theories, Algebraic Categories, and Algebraic Functors, {\em Theory of Models}, Amsterdam: North Holland, 413--418. |
Lawvere, F. W., 1965, Algebraic Theories, Algebraic Categories, and Algebraic Functors, {\em Theory of Models}, Amsterdam: North Holland, 413--418. |
|
|
| \bibitem{LFW66} |
\bibitem{LFW66} |
| Lawvere, F. W.: 1966, The Category of Categories as a Foundation for Mathematics., in |
Lawvere, F. W.: 1966, The Category of Categories as a Foundation for Mathematics., in |
| \emph{Proc. Conf. Categorical Algebra- La Jolla}., Eilenberg, S. et al., eds. Springer--Verlag: |
\emph{Proc. Conf. Categorical Algebra- La Jolla}., Eilenberg, S. et al., eds. Springer--Verlag: |
| Berlin, Heidelberg and New York., pp. 1-20. |
Berlin, Heidelberg and New York., pp. 1-20. |
|
|
| \bibitem{LFW69a} |
\bibitem{LFW69a} |
| Lawvere, F. W., 1969a, Diagonal Arguments and Cartesian Closed Categories, in {\em Category Theory, Homology Theory, and their Applications II}, Berlin: Springer, 134--145. |
Lawvere, F. W., 1969a, Diagonal Arguments and Cartesian Closed Categories, in {\em Category Theory, Homology Theory, and their Applications II}, Berlin: Springer, 134--145. |
|
|
| \bibitem{LFW69b} |
\bibitem{LFW69b} |
| Lawvere, F. W., 1969b, Adjointness in Foundations, {\em Dialectica}, \textbf{23}: 281--295. |
Lawvere, F. W., 1969b, Adjointness in Foundations, {\em Dialectica}, \textbf{23}: 281--295. |
|
|
| \bibitem{LFW70} |
\bibitem{LFW70} |
| Lawvere, F. W., 1970, Equality in Hyper doctrines and Comprehension Schema as an Adjoint Functor, |
Lawvere, F. W., 1970, Equality in Hyper doctrines and Comprehension Schema as an Adjoint Functor, |
| {\em Applications of Categorical Algebra}, Providence: AMS, 1-14. |
{\em Applications of Categorical Algebra}, Providence: AMS, 1-14. |
|
|
| \bibitem{LT271} |
\bibitem{LT271} |
| Lawvere, F. W., 1971, Quantifiers and Sheaves, {\em Actes du Congr\'es International des Math\'ematiciens}, Tome 1, Paris: Gauthier-Villars, 329--334. |
Lawvere, F. W., 1971, Quantifiers and Sheaves, {\em Actes du Congr\'es International des Math\'ematiciens}, Tome 1, Paris: Gauthier-Villars, 329--334. |
|
|
| \bibitem{LFW72} |
\bibitem{LFW72} |
| Lawvere, F. W., 1972, Introduction, in {\em Toposes, Algebraic Geometry and Logic}, Lecture Notes in Mathematics, 274, Springer-Verlag, 1-12. |
Lawvere, F. W., 1972, Introduction, in {\em Toposes, Algebraic Geometry and Logic}, Lecture Notes in Mathematics, 274, Springer-Verlag, 1-12. |
|
|
| \bibitem{LFW75} |
\bibitem{LFW75} |
| Lawvere, F. W., 1975, Continuously Variable Sets: Algebraic Geometry = Geometric Logic, {\em Proceedings of the Logic Colloquium}, Bristol 1973, Amsterdam: North Holland, 135-153. |
Lawvere, F. W., 1975, Continuously Variable Sets: Algebraic Geometry = Geometric Logic, {\em Proceedings of the Logic Colloquium}, Bristol 1973, Amsterdam: North Holland, 135-153. |
|
|
| \bibitem{LFW76} |
\bibitem{LFW76} |
| Lawvere, F. W., 1976, Variable Quantities and Variable Structures, in {\em Topoi, Algebra, Topology, and Category Theory}, New York: Academic Press, 101--131. |
Lawvere, F. W., 1976, Variable Quantities and Variable Structures, in {\em Topoi, Algebra, Topology, and Category Theory}, New York: Academic Press, 101--131. |
|
|
| \bibitem{LFW63} |
\bibitem{LFW63} |
| Lawvere, F. W.: 1963, Functorial Semantics of Algebraic Theories, \emph{Proc. Natl. Acad. Sci. USA, Mathematics}, \textbf{50}: 869-872. |
Lawvere, F. W.: 1963, Functorial Semantics of Algebraic Theories, \emph{Proc. Natl. Acad. Sci. USA, Mathematics}, \textbf{50}: 869-872. |
|
|
| \bibitem{LFW92} |
\bibitem{LFW92} |
| Lawvere, F. W., 1992, Categories of Space and of Quantity, {\em The Space of Mathematics, Foundations of Communication and Cognition}, Berlin: De Gruyter, 14-30. |
Lawvere, F. W., 1992, Categories of Space and of Quantity, {\em The Space of Mathematics, Foundations of Communication and Cognition}, Berlin: De Gruyter, 14-30. |
|
|
| \bibitem{LFW94b} |
\bibitem{LFW94b} |
| Lawvere, F. W., 1994b, Tools for the Advancement of Objective Logic: Closed Categories and Toposes, |
Lawvere, F. W., 1994b, Tools for the Advancement of Objective Logic: Closed Categories and Toposes, |
| {\em The Logical Foundations of Cognition}, Vancouver Studies in Cognitive Science, 4, Oxford: Oxford University Press, 43--56. |
{\em The Logical Foundations of Cognition}, Vancouver Studies in Cognitive Science, 4, Oxford: Oxford University Press, 43--56. |
|
|
| \bibitem{LFW2k} |
\bibitem{LFW2k} |
| Lawvere, F. W., 2000, Comments on the Development of Topos Theory, {\em Development of Mathematics 1950-2000}, Basel: Birkh\''auser, 715--734. |
Lawvere, F. W., 2000, Comments on the Development of Topos Theory, {\em Development of Mathematics 1950-2000}, Basel: Birkh\''auser, 715--734. |
|
|
| \bibitem{LFW2k2} |
\bibitem{LFW2k2} |
| Lawvere, F. W., 2002, Categorical Algebra for Continuum Micro-Physics, {\em Journal of Pure and Applied Algebra}, 175, no. 1--3, 267--287. |
Lawvere, F. W., 2002, Categorical Algebra for Continuum Micro-Physics, {\em Journal of Pure and Applied Algebra}, 175, no. 1--3, 267--287. |
|
|
| \bibitem{LFWk3} |
\bibitem{LFWk3} |
| Lawvere, F. W., 2003, Foundations and Applications: Axiomatization and Education. New Programs and Open Problems in the Foundation of Mathematics, {\em Bulletin of Symbolic Logic}, 9, 2, 213--224. |
Lawvere, F. W., 2003, Foundations and Applications: Axiomatization and Education. New Programs and Open Problems in the Foundation of Mathematics, {\em Bulletin of Symbolic Logic}, 9, 2, 213--224. |
|
|
| \bibitem{LT2k2} |
\bibitem{LT2k2} |
| Leinster, T., 2002, A Survey of Definitions of n-categories, in {Theory and Applications of Categories}, (electronic), \textbf{10}, 1--70. |
Leinster, T., 2002, A Survey of Definitions of n-categories, in {Theory and Applications of Categories}, (electronic), \textbf{10}, 1--70. |
|
|
| \bibitem{LiM-PV97} |
\bibitem{LiM-PV97} |
| Li, M. and P. Vitanyi: 1997, \emph{An introduction to Kolmogorov Complexity and its Applications}, Springer Verlag: New York. |
Li, M. and P. Vitanyi: 1997, \emph{An introduction to Kolmogorov Complexity and its Applications}, Springer Verlag: New York. |
|
|
| \bibitem{Lofgren68} |
\bibitem{Lofgren68} |
| L\''{o}fgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction, \emph{Bulletin of Mathematical Biophysics}, \textbf{30}: 317-348 |
L\''{o}fgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction, \emph{Bulletin of Mathematical Biophysics}, \textbf{30}: 317-348 |
|
|
| \bibitem{LS60} |
\bibitem{LS60} |
| Lubkin, S., 1960. Imbedding of abelian categories., {\em Trans. Amer. Math. Soc.}, \textbf{97}: 410-417. |
Lubkin, S., 1960. Imbedding of abelian categories., {\em Trans. Amer. Math. Soc.}, \textbf{97}: 410-417. |
|
|
|
|
| \bibitem{Mack1} |
\bibitem{Mack1} |
| K. C. H. Mackenzie : {\em Lie Groupoids and Lie Algebroids in Differential Geometry}, LMS Lect. Notes \textbf{124}, Cambridge University Press, 1987 |
K. C. H. Mackenzie : {\em Lie Groupoids and Lie Algebroids in Differential Geometry}, LMS Lect. Notes \textbf{124}, Cambridge University Press, 1987 |
|
|
| \bibitem{MCLSS48} |
\bibitem{MCLSS48} |
| MacLane, S.: 1948. Groups, categories, and duality., {\em Proc. Natl. Acad. Sci.U.S.A}, \textbf{34}: 263-267. |
MacLane, S.: 1948. Groups, categories, and duality., {\em Proc. Natl. Acad. Sci.U.S.A}, \textbf{34}: 263-267. |
|
|
| \bibitem{MCLSS69} |
\bibitem{MCLSS69} |
| MacLane, S., 1969, Foundations for Categories and Sets, in {\em Category Theory, Homology Theory and their Applications II}, Berlin: Springer, 146--164. |
MacLane, S., 1969, Foundations for Categories and Sets, in {\em Category Theory, Homology Theory and their Applications II}, Berlin: Springer, 146--164. |
|
|
| \bibitem{MCLS71}MacLane, S., 1971, Categorical algebra and Set-Theoretic Foundations, in {\em Axiomatic Set Theory}, Providence: AMS, 231--240. |
\bibitem{MCLS71}MacLane, S., 1971, Categorical algebra and Set-Theoretic Foundations, in {\em Axiomatic Set Theory}, Providence: AMS, 231--240. |
|
|
| \bibitem{MCLS75} |
\bibitem{MCLS75} |
| MacLane, S., 1975, Sets, Topoi, and Internal Logic in Categories, {\em Studies in Logic and the Foundations of Mathematics}, 80, Amsterdam: North Holland, 119--134. |
MacLane, S., 1975, Sets, Topoi, and Internal Logic in Categories, {\em Studies in Logic and the Foundations of Mathematics}, 80, Amsterdam: North Holland, 119--134. |
|
|
| \bibitem{MCLS86} |
\bibitem{MCLS86} |
| MacLane, S., 1986, {\em Mathematics, Form and Function}, New York: Springer. |
MacLane, S., 1986, {\em Mathematics, Form and Function}, New York: Springer. |
|
|
| \bibitem{MCLS88} |
\bibitem{MCLS88} |
| MacLane, S., 1988, Concepts and Categories in Perspective, in {\em A Century of Mathematics in America, Part I}, Providence: AMS, 323--365. |
MacLane, S., 1988, Concepts and Categories in Perspective, in {\em A Century of Mathematics in America, Part I}, Providence: AMS, 323--365. |
|
|
| \bibitem{MCLS89} |
\bibitem{MCLS89} |
| MacLane, S., 1989, The Development of Mathematical Ideas by Collision: the Case of Categories and Topos Theory, in {\em Categorical Topology and its Relation to Analysis, Algebra and Combinatorics}, Teaneck: World Scientific, 1--9. |
MacLane, S., 1989, The Development of Mathematical Ideas by Collision: the Case of Categories and Topos Theory, in {\em Categorical Topology and its Relation to Analysis, Algebra and Combinatorics}, Teaneck: World Scientific, 1--9. |
|
|
| \bibitem{MS-IM92} |
\bibitem{MS-IM92} |
| Maclane, S. and I. Moerdijk : {\em Sheaves in Geometry and Logic -- A first Introduction to Topos Theory}, Springer Verlag, New York |
Maclane, S. and I. Moerdijk : {\em Sheaves in Geometry and Logic -- A first Introduction to Topos Theory}, Springer Verlag, New York |
| 1992. |
1992. |
|
|
| \bibitem{MLS50} |
\bibitem{MLS50} |
| MacLane, S., 1950, Dualities for Groups, {\em Bulletin of the American Mathematical Society}, 56, 485-516. |
MacLane, S., 1950, Dualities for Groups, {\em Bulletin of the American Mathematical Society}, 56, 485-516. |
|
|
| \bibitem{MCLS96} |
\bibitem{MCLS96} |
| MacLane, S., 1996, Structure in Mathematics. Mathematical Structuralism., {\em Philosophia Mathematica}, 4, 2, 174-183. |
MacLane, S., 1996, Structure in Mathematics. Mathematical Structuralism., {\em Philosophia Mathematica}, 4, 2, 174-183. |
|
|
| \bibitem{MCLS98} |
\bibitem{MCLS98} |
| MacLane, S., 1997, Categories for the Working Mathematician, 2nd edition, New York: Springer-Verlag. |
MacLane, S., 1997, Categories for the Working Mathematician, 2nd edition, New York: Springer-Verlag. |
|
|
| \bibitem{Majid1} |
\bibitem{Majid1} |
| Majid, S.: 1995, \emph{Foundations of Quantum Group Theory}, Cambridge Univ. Press: Cambridge, UK. |
Majid, S.: 1995, \emph{Foundations of Quantum Group Theory}, Cambridge Univ. Press: Cambridge, UK. |
|
|
| \bibitem{Majid2} |
\bibitem{Majid2} |
| Majid, S.: 2002, \emph{A Quantum Groups Primer}, Cambridge Univ.Press: Cambridge, UK. |
Majid, S.: 2002, \emph{A Quantum Groups Primer}, Cambridge Univ.Press: Cambridge, UK. |
|
|
| \bibitem{MM-RG95} |
\bibitem{MM-RG95} |
| Makkai, M. \& Par\'e, R., 1989, {\em Accessible Categories: the Foundations of Categorical Model Theory, Contemporary Mathematics}, 104, Providence: AMS. |
Makkai, M. \& Par\'e, R., 1989, {\em Accessible Categories: the Foundations of Categorical Model Theory, Contemporary Mathematics}, 104, Providence: AMS. |
|
|
| \bibitem{MM99} |
\bibitem{MM99} |
| Makkai, M., 1999, On Structuralism in Mathematics, in {\em Language, Logic and Concepts}, Cambridge: MIT Press, 43--66. |
Makkai, M., 1999, On Structuralism in Mathematics, in {\em Language, Logic and Concepts}, Cambridge: MIT Press, 43--66. |
|
|
| \bibitem{MM-RG77} |
\bibitem{MM-RG77} |
| Makkai, M. \& Reyes, G., 1977, {\em First-Order Categorical Logic}, Springer Lecture Notes in Mathematics 611, New York: Springer. |
Makkai, M. \& Reyes, G., 1977, {\em First-Order Categorical Logic}, Springer Lecture Notes in Mathematics 611, New York: Springer. |
|
|
| \bibitem{MM-RG95} |
\bibitem{MM-RG95} |
| Makkei, M. \& Reyes, G., 1995, Completeness Results for Intuitionistic and Modal Logic in a Categorical Setting, |
Makkei, M. \& Reyes, G., 1995, Completeness Results for Intuitionistic and Modal Logic in a Categorical Setting, |
| {\em Annals of Pure and Applied Logic}, 72, 1, 25--101. |
{\em Annals of Pure and Applied Logic}, 72, 1, 25--101. |
|
|
| \bibitem{MJP93} |
\bibitem{MJP93} |
| Marquis, J.-P., 1993, Russell's Logicism and Categorical Logicisms, in {\em Russell and Analytic Philosophy}, A. D. Irvine \& G. A. Wedekind, (eds.), Toronto, University of Toronto Press, 293--324. |
Marquis, J.-P., 1993, Russell's Logicism and Categorical Logicisms, in {\em Russell and Analytic Philosophy}, A. D. Irvine \& G. A. Wedekind, (eds.), Toronto, University of Toronto Press, 293--324. |
|
|
| \bibitem{MJP95} |
\bibitem{MJP95} |
| Marquis, J.-P., 1995, Category Theory and the Foundations of Mathematics: Philosophical Excavations., |
Marquis, J.-P., 1995, Category Theory and the Foundations of Mathematics: Philosophical Excavations., |
| {\em Synthese}, 103, 421--447. |
{\em Synthese}, 103, 421--447. |
|
|
| \bibitem{MJP2k6} |
\bibitem{MJP2k6} |
| Marquis, J.-P., 2006, Categories, Sets and the Nature of Mathematical Entities, in {\em The Age of Alternative Logics. Assessing philosophy of logic and mathematics today}, J. van Benthem, G. Heinzmann, Ph. Nabonnand, M. Rebuschi, H.Visser, eds., Springer,181-192. |
Marquis, J.-P., 2006, Categories, Sets and the Nature of Mathematical Entities, in {\em The Age of Alternative Logics. Assessing philosophy of logic and mathematics today}, J. van Benthem, G. Heinzmann, Ph. Nabonnand, M. Rebuschi, H.Visser, eds., Springer,181-192. |
|
|
| \bibitem{MJP1999} |
\bibitem{MJP1999} |
| May, J.P. 1999, \emph{A Concise Course in Algebraic Topology}, The University of Chicago Press: Chicago. |
May, J.P. 1999, \emph{A Concise Course in Algebraic Topology}, The University of Chicago Press: Chicago. |
|
|
| \bibitem{MCWP43} |
\bibitem{MCWP43} |
| McCulloch, W. and W. Pitt.: 1943, A logical Calculus of Ideas Immanent in Nervous Activity., \emph{Bull. Math. Biophysics,} \textbf{5}: 115-133. |
McCulloch, W. and W. Pitt.: 1943, A logical Calculus of Ideas Immanent in Nervous Activity., \emph{Bull. Math. Biophysics,} \textbf{5}: 115-133. |
|
|
| \bibitem{MLC86} |
\bibitem{MLC86} |
| Mc Larty, C., 1986, Left Exact Logic, {\em Journal of Pure and Applied Algebra}, 41, no. 1, 63-66. |
Mc Larty, C., 1986, Left Exact Logic, {\em Journal of Pure and Applied Algebra}, 41, no. 1, 63-66. |
|
|
| \bibitem{MLC91} |
\bibitem{MLC91} |
| Mc Larty, C., 1991, Axiomatizing a Category of Categories, {\em Journal of Symbolic Logic}, 56, no. 4, 1243-1260. |
Mc Larty, C., 1991, Axiomatizing a Category of Categories, {\em Journal of Symbolic Logic}, 56, no. 4, 1243-1260. |
|
|
| \bibitem{MLC92} |
\bibitem{MLC92} |
| Mc Larty, C., 1992, {\em Elementary Categories, Elementary Toposes}, Oxford: Oxford University Press. |
Mc Larty, C., 1992, {\em Elementary Categories, Elementary Toposes}, Oxford: Oxford University Press. |
|
|
| \bibitem{MLC94} |
\bibitem{MLC94} |
| Mc Larty, C., 1994, Category Theory in Real Time, {\em Philosophia Mathematica}, \textbf{2}, no. 1, 36-44. |
Mc Larty, C., 1994, Category Theory in Real Time, {\em Philosophia Mathematica}, \textbf{2}, no. 1, 36-44. |
|
|
| \bibitem{MLC2k5} |
\bibitem{MLC2k5} |
| Mc Larty, C., 2005, Learning from Questions on Categorical Foundations, {\em Philosophia Mathematica}, \textbf{13}, 1, 44--60. |
Mc Larty, C., 2005, Learning from Questions on Categorical Foundations, {\em Philosophia Mathematica}, \textbf{13}, 1, 44--60. |
|
|
| \bibitem{Mitchell1} |
\bibitem{Mitchell1} |
| Mitchell, B.: 1965, \emph{Theory of Categories}, Academic Press:London. |
Mitchell, B.: 1965, \emph{Theory of Categories}, Academic Press:London. |
|
|
| \bibitem{Mitchell2} |
\bibitem{Mitchell2} |
| Mitchell, B.: 1964, The full imbedding theorem. \emph{Amer. J. Math}. \textbf{86}: 619-637. |
Mitchell, B.: 1964, The full imbedding theorem. \emph{Amer. J. Math}. \textbf{86}: 619-637. |
|
|
| \bibitem{MI-P2k2} |
\bibitem{MI-P2k2} |
| Moerdijk, I. \& Palmgren, E., 2002, Type Theories, Toposes and Constructive Set Theory: Predicative Aspects of AST., Annals of Pure and Applied Logic, 114, no. 1--3, 155--201. |
Moerdijk, I. \& Palmgren, E., 2002, Type Theories, Toposes and Constructive Set Theory: Predicative Aspects of AST., Annals of Pure and Applied Logic, 114, no. 1--3, 155--201. |
|
|
| \bibitem{MO98} |
\bibitem{MO98} |
| Moerdijk, I., 1998, Sets, Topoi and Intuitionism., Philosophia Mathematica, 6, no. 2, 169-177. |
Moerdijk, I., 1998, Sets, Topoi and Intuitionism., Philosophia Mathematica, 6, no. 2, 169-177. |
|
|
| \bibitem{Moer1} |
\bibitem{Moer1} |
| I. Moerdijk : Classifying toposes and foliations, {\it Ann. Inst. Fourier, Grenoble} \textbf{41}, 1 (1991) 189-209. |
I. Moerdijk : Classifying toposes and foliations, {\it Ann. Inst. Fourier, Grenoble} \textbf{41}, 1 (1991) 189-209. |
|
|
| \bibitem{Moer2} |
\bibitem{Moer2} |
| I. Moerdijk : Introduction to the language of stacks and gerbes, (preprint at arXiv:math.AT/0212266) (2002). |
I. Moerdijk : Introduction to the language of stacks and gerbes, (preprint at arXiv:math.AT/0212266) (2002). |
|
|
| \bibitem{MK62} |
\bibitem{MK62} |
| Morita, K. 1962. Category isomorphism and endomorphism rings of modules, |
Morita, K. 1962. Category isomorphism and endomorphism rings of modules, |
| {\em Trans. Amer. Math. Soc.}, \textbf{103}: 451-469. |
{\em Trans. Amer. Math. Soc.}, \textbf{103}: 451-469. |
|
|
| \bibitem{MK70} |
\bibitem{MK70} |
| Morita, K. , 1970. Localization in categories of modules. I., {\em Math. Z.}, |
Morita, K. , 1970. Localization in categories of modules. I., {\em Math. Z.}, |
| \textbf{114}: 121-144. |
\textbf{114}: 121-144. |
|
|
| \bibitem{Mostow} |
\bibitem{Mostow} |
| M. A. Mostow : The differentiable space structure of Milnor classifying spaces, simplicial complexes, and geometric |
M. A. Mostow : The differentiable space structure of Milnor classifying spaces, simplicial complexes, and geometric |
| realizations, \emph{J. Diff. Geom.} \textbf{14} (1979) 255-293. |
realizations, \emph{J. Diff. Geom.} \textbf{14} (1979) 255-293. |
|
|
| \bibitem{OB69} |
\bibitem{OB69} |
| Oberst, U.: 1969, Duality theory for Grothendieck categories., \emph{Bull. Amer. Math. Soc.} \textbf{75}: 1401-1408. |
Oberst, U.: 1969, Duality theory for Grothendieck categories., \emph{Bull. Amer. Math. Soc.} \textbf{75}: 1401-1408. |
|
|
| \bibitem{ORT70} |
\bibitem{ORT70} |
| Oort, F.: 1970. On the definition of an abelian category. \emph{Proc. Roy. Neth. Acad. Sci}. \textbf{70}: 13-02. |
Oort, F.: 1970. On the definition of an abelian category. \emph{Proc. Roy. Neth. Acad. Sci}. \textbf{70}: 13-02. |
|
|
| \bibitem{OO31} |
\bibitem{OO31} |
| Ore, O., 1931, Linear equations on non-commutative fields, {\em Ann. Math.} \textbf{32}: 463-477. |
Ore, O., 1931, Linear equations on non-commutative fields, {\em Ann. Math.} \textbf{32}: 463-477. |
|
|
| \bibitem{PLR} |
\bibitem{PLR} |
| Plymen, R.J. and P. L. Robinson: 1994, \emph{Spinors in Hilbert Space}, Cambridge Tracts in Math. |
Plymen, R.J. and P. L. Robinson: 1994, \emph{Spinors in Hilbert Space}, Cambridge Tracts in Math. |
| \textbf{114}, Cambridge Univ. Press, Cambridge. |
\textbf{114}, Cambridge Univ. Press, Cambridge. |
|
|
| \bibitem{NPop1} |
\bibitem{NPop1} |
| Popescu, N.: 1973, \emph{Abelian Categories with Applications to Rings and Modules.} New York and London: Academic Press., 2nd edn. 1975. \emph{(English translation by I.C. Baianu)}. |
Popescu, N.: 1973, \emph{Abelian Categories with Applications to Rings and Modules.} New York and London: Academic Press., 2nd edn. 1975. \emph{(English translation by I.C. Baianu)}. |
|
|
| \bibitem{PB70} |
\bibitem{PB70} |
| Pareigis, B., 1970, Categories and Functors, New York: Academic Press. |
Pareigis, B., 1970, Categories and Functors, New York: Academic Press. |
|
|
| \bibitem{PMC2k4} |
\bibitem{PMC2k4} |
| Pedicchio, M. C. and Tholen, W., 2004, Categorical Foundations, Cambridge: Cambridge University Press. |
Pedicchio, M. C. and Tholen, W., 2004, Categorical Foundations, Cambridge: Cambridge University Press. |
|
|
| \bibitem{PB91} |
\bibitem{PB91} |
| Peirce, B., 1991, Basic Category Theory for Computer Scientists, Cambridge: MIT Press. |
Peirce, B., 1991, Basic Category Theory for Computer Scientists, Cambridge: MIT Press. |
|
|
| \bibitem{PAM90} |
\bibitem{PAM90} |
| Pitts, A. M., 1989, Conceptual Completeness for First-order Intuitionistic Logic: an Application of Categorical Logic, |
Pitts, A. M., 1989, Conceptual Completeness for First-order Intuitionistic Logic: an Application of Categorical Logic, |
| {\em Annals of Pure and Applied Logic}, 41, no. 1, 33--81. |
{\em Annals of Pure and Applied Logic}, 41, no. 1, 33--81. |
|
|
| \bibitem{PAM2k} |
\bibitem{PAM2k} |
| Pitts, A. M., 2000, {\em Categorical Logic}, in {\em Handbook of Logic in Computer Science}, Vol.5, Oxford: Oxford Unversity Press, 39-128. |
Pitts, A. M., 2000, {\em Categorical Logic}, in {\em Handbook of Logic in Computer Science}, Vol.5, Oxford: Oxford Unversity Press, 39-128. |
|
|
| \bibitem{PB2k} |
\bibitem{PB2k} |
| Plotkin, B., 2000, Algebra, Categories and Databases, in {\em Handbook of Algebra}, Vol. 2, Amsterdam: Elsevier, 79--148. |
Plotkin, B., 2000, Algebra, Categories and Databases, in {\em Handbook of Algebra}, Vol. 2, Amsterdam: Elsevier, 79--148. |
|
|
| \bibitem{Pradines1966} |
\bibitem{Pradines1966} |
| Pradines, J.: 1966, Th\'eorie de Lie pour les groupoides diff\'erentiable, relation entre propri\'etes locales et globales, \emph{C. R. Acad Sci. Paris S\'er. A} \textbf{268}: 907-910. |
Pradines, J.: 1966, Th\'eorie de Lie pour les groupoides diff\'erentiable, relation entre propri\'etes locales et globales, \emph{C. R. Acad Sci. Paris S\'er. A} \textbf{268}: 907-910. |
|
|
| \bibitem{Raptis1-2k3} |
\bibitem{Raptis1-2k3} |
| Raptis, I.: 2003, Algebraic quantisation of causal sets, \emph{Int. Jour. Theor. Phys.} \textbf{39}: 1233. |
Raptis, I.: 2003, Algebraic quantisation of causal sets, \emph{Int. Jour. Theor. Phys.} \textbf{39}: 1233. |
|
|
| \bibitem{RGZH91} |
\bibitem{RGZH91} |
| Reyes, G. \& Zolfaghari, H., 1991, Topos-theoretic Approaches to Modality,in {\em Category Theory (Como 1990), Lecture Notes in Mathematics}, 1488, Berlin: Springer, 359--378. |
Reyes, G. \& Zolfaghari, H., 1991, Topos-theoretic Approaches to Modality,in {\em Category Theory (Como 1990), Lecture Notes in Mathematics}, 1488, Berlin: Springer, 359--378. |
|
|
| \bibitem{RGZH96} |
\bibitem{RGZH96} |
| Reyes, G. \& Zolfaghari, H., 1996, Bi-Heyting Algebras, Toposes and Modalities, in {\em Journal of Philosophical Logic}, 25, no. 1, 25-43. |
Reyes, G. \& Zolfaghari, H., 1996, Bi-Heyting Algebras, Toposes and Modalities, in {\em Journal of Philosophical Logic}, 25, no. 1, 25-43. |
|
|
| \bibitem{RG74} |
\bibitem{RG74} |
| Reyes, G., 1974, From Sheaves to Logic, in {\em Studies in Algebraic Logic}, A. Daigneault, ed., Providence: AMS. |
Reyes, G., 1974, From Sheaves to Logic, in {\em Studies in Algebraic Logic}, A. Daigneault, ed., Providence: AMS. |
|
|
| \bibitem{Rieffel} |
\bibitem{Rieffel} |
| M. A. Rieffel : Group C*-algebras as compact quantum metric spaces, \emph{Documenta Math.} \textbf{7} (2002), 605-651. |
M. A. Rieffel : Group C*-algebras as compact quantum metric spaces, \emph{Documenta Math.} \textbf{7} (2002), 605-651. |
|
|
| \bibitem{Roberts} |
\bibitem{Roberts} |
| Roberts, J. E.: 2004, More lectures on algebraic quantum field theory, in A. Connes, et al. \emph{Noncommutative Geometry}, Springer: Berlin and New York. |
Roberts, J. E.: 2004, More lectures on algebraic quantum field theory, in A. Connes, et al. \emph{Noncommutative Geometry}, Springer: Berlin and New York. |
|
|
| \bibitem{RSE-KEP94} |
\bibitem{RSE-KEP94} |
| Rodabaugh, S. E. \& Klement, E. P., eds., Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic, 20, Dordrecht: Kluwer. |
Rodabaugh, S. E. \& Klement, E. P., eds., Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic, 20, Dordrecht: Kluwer. |
|
|
|
|
| \bibitem{RRosen2} |
\bibitem{RRosen2} |
| Rosen, R.: 1958b, The Representation of Biological Systems from the Standpoint of the Theory of Categories., \emph{ Bulletin of Mathematical Biophysics} \textbf{20}: 317-341. |
Rosen, R.: 1958b, The Representation of Biological Systems from the Standpoint of the Theory of Categories., \emph{ Bulletin of Mathematical Biophysics} \textbf{20}: 317-341. |
|
|
| \bibitem{Rota} G. C. Rota : On the foundation of combinatorial theory, I. The theory of M\"obius functions, \emph{Zetschrif f\''ur Wahrscheinlichkeitstheorie} \textbf{2} (1968), 340. |
\bibitem{Rota} G. C. Rota : On the foundation of combinatorial theory, I. The theory of M\"obius functions, \emph{Zetschrif f\''ur Wahrscheinlichkeitstheorie} \textbf{2} (1968), 340. |
|
|
| \bibitem{SPJ2k} |
\bibitem{SPJ2k} |
| Scott, P. J., 2000, {\em Some Aspects of Categories in Computer Science}, Handbook of Algebra, Vol. 2, Amsterdam: North Holland, 3--77. |
Scott, P. J., 2000, {\em Some Aspects of Categories in Computer Science}, Handbook of Algebra, Vol. 2, Amsterdam: North Holland, 3--77. |
|
|
| \bibitem{SHS2k5} |
\bibitem{SHS2k5} |
| Shapiro, S., 2005, Categories, Structures and the Frege-Hilbert Controversy: the Status of Metamathematics, |
Shapiro, S., 2005, Categories, Structures and the Frege-Hilbert Controversy: the Status of Metamathematics, |
| {\em Philosophia Mathematica}, 13, 1, 61--77. |
{\em Philosophia Mathematica}, 13, 1, 61--77. |
|
|
| \bibitem{Sorkin} |
\bibitem{Sorkin} |
| Sorkin, R.D.: 1991, Finitary substitute for continuous topology, \emph{Int. J. Theor. Phys.} \textbf{30} No. 7.: 923--947. |
Sorkin, R.D.: 1991, Finitary substitute for continuous topology, \emph{Int. J. Theor. Phys.} \textbf{30} No. 7.: 923--947. |
|
|
| \bibitem{Spanier} |
\bibitem{Spanier} |
| Spanier, E. H.: 1966, \emph{Algebraic Topology}, McGraw Hill: New York. |
Spanier, E. H.: 1966, \emph{Algebraic Topology}, McGraw Hill: New York. |
|
|
| \bibitem{Szabo} |
\bibitem{Szabo} |
| Szabo, R. J.: 2003, Quantum field theory on non-commutative spaces, \emph{Phys. Rep.} \textbf{378}: 207--209. |
Szabo, R. J.: 2003, Quantum field theory on non-commutative spaces, \emph{Phys. Rep.} \textbf{378}: 207--209. |
|
|
| \bibitem{Thom80} |
\bibitem{Thom80} |
| Thom, R.: 1980, \emph{Mod\`eles math\'ematiques de la morphog\'en\`ese}, Paris, Bourgeois. |
Thom, R.: 1980, \emph{Mod\`eles math\'ematiques de la morphog\'en\`ese}, Paris, Bourgeois. |
|
|
| \bibitem{TP96} |
\bibitem{TP96} |
| Taylor, P., 1996, Intuitionistic sets and Ordinals, {\em Journal of Symbolic Logic}, 61, 705--744. |
Taylor, P., 1996, Intuitionistic sets and Ordinals, {\em Journal of Symbolic Logic}, 61, 705--744. |
| |
|
| \bibitem{TP99} |
\bibitem{TP99} |
| Taylor, P., 1999, Practical Foundations of Mathematics, Cambridge: Cambridge University Press. |
Taylor, P., 1999, Practical Foundations of Mathematics, Cambridge: Cambridge University Press. |
|
|
| \bibitem{TP72} |
\bibitem{TP72} |
| Tierney, M., 1972, Sheaf Theory and the Continuum Hypothesis, {\em Toposes, Algebraic Geometry and Logic}. |
Tierney, M., 1972, Sheaf Theory and the Continuum Hypothesis, {\em Toposes, Algebraic Geometry and Logic}. |
|
|
| \bibitem{VdHG-MI84a} |
\bibitem{VdHG-MI84a} |
| Van der Hoeven, G. and Moerdijk, I., 1984a, Sheaf Models for Choice Sequences, |
Van der Hoeven, G. and Moerdijk, I., 1984a, Sheaf Models for Choice Sequences, |
| {\em Annals of Pure and Applied Logic}, 27, no. 1, 63--107. |
{\em Annals of Pure and Applied Logic}, 27, no. 1, 63--107. |
|
|
| \bibitem{Varilly} |
\bibitem{Varilly} |
| V\'arilly, J. C.: 1997, An introduction to noncommutative geometry. (at arXiv:physics/9709045) |
V\'arilly, J. C.: 1997, An introduction to noncommutative geometry. (at arXiv:physics/9709045) |
|
|
| \bibitem{Weinstein96} |
\bibitem{Weinstein96} |
| Weinstein, A.: 1996, Groupoids : unifying internal and external symmetry, \emph{Notices of the Amer. Math. Soc.} \textbf{43}: 744--752. |
Weinstein, A.: 1996, Groupoids : unifying internal and external symmetry, \emph{Notices of the Amer. Math. Soc.} \textbf{43}: 744--752. |
|
|
| \bibitem{WB83} |
\bibitem{WB83} |
| Wess J. and J. Bagger: 1983, \emph{Supersymmetry and Supergravity}, Princeton University Press: Princeton, NJ. |
Wess J. and J. Bagger: 1983, \emph{Supersymmetry and Supergravity}, Princeton University Press: Princeton, NJ. |
|
|
| \bibitem{Whitehead1941} |
\bibitem{Whitehead1941} |
| Whitehead, J. H. C.: 1941, On adding relations to homotopy groups, \emph{Annals of Math.} \textbf{42} (2): 409--428. |
Whitehead, J. H. C.: 1941, On adding relations to homotopy groups, \emph{Annals of Math.} \textbf{42} (2): 409--428. |
|
|
| \bibitem{WRJ2k4} |
\bibitem{WRJ2k4} |
| Wood, R.J., 2004, Ordered Sets via Adjunctions, in {\em Categorical Foundations}, M. C. Pedicchio and W. Tholen, eds., Cambridge: Cambridge University Press. |
Wood, R.J., 2004, Ordered Sets via Adjunctions, in {\em Categorical Foundations}, M. C. Pedicchio and W. Tholen, eds., Cambridge: Cambridge University Press. |
|
|
| \end{thebibliography} |
\end{thebibliography} |
|
|
|
|
