bibliography for axiomatics and mathematics foundations in categories


0.1 A Bibliography for Axiomatic Theories and Categorical Foundations of Mathematical Physics and Mathematics

0.1.1 a. Foundations of Mathematics, Logics and Formal Logics (http://planetmath.org/AnalyticsAndOntologyFormalLogics): Axiomatics, Categories, Topoi and Higher Dimensional Algebra (http://planetmath.org/HigherDimensionalAlgebraHDA)

References

  • 1 Awodey, S. 1996. “StructureMathworldPlanetmath in Mathematics and Logic: A Categorical Perspective.”, Philosophia Mathematica, 3, 209–237.
  • 2 Awodey, S., 2006, Category TheoryMathworldPlanetmathPlanetmathPlanetmathPlanetmath, Oxford: Clarendon Press.
  • 3 Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. n-CategoriesMathworldPlanetmath and the AlgebraMathworldPlanetmathPlanetmath of Opetopes, Advances in Mathematics, 135: 145–206.
  • 4 Baez, J. and Dolan, J., 1998b, “Categorification”, Higher Category Theory, Contemporary Mathematics, 230, Providence: AMS, 1–36.
  • 5 Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional AlgebraPlanetmathPlanetmath and Łukasiewicz-Moisil Topos: TransformationsPlanetmathPlanetmath of Neuronal, Genetic and Neoplastic Networks., Axiomathes, 16 Nos. 1-2: 65-122.
  • 6 Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems. Bulletin of Mathematical Biophysics, 35(4): 475-486.
  • 7 Baianu, I. C., Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum Automata and N-Valued Łukasiewicz Algebras in RelationMathworldPlanetmathPlanetmathPlanetmath to Dynamic Bionetworks, (M,R)-Systems and Their Higher Dimensional Algebra, Preprint of Report.
  • 8 Barr, M. and C. Wells. Toposes, Triples and Theories. Montreal: McGill University, 2000.
  • 9 Barr, M. and Wells, C. 1999.Category Theory for Computing Science, Montreal: CRM.
  • 10 Batanin, M. 1998. Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories., Advances in Mathematics, 136, 39–103.
  • 11 Bell, J. L. 1981. Category Theory and the Foundations of Mathematics, British Journal for the Philosophy of Science, 32, 349–358.
  • 12 Bell, J. L., 1982. Categories, Toposes and Sets, Synthese, 51(3): 293–337.
  • 13 Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite ForcingMathworldPlanetmath , Journal of Pure and Applied Algebra, 28, 111–140.
  • 14 Blass, A. and Scedrov, A., 1989, Freyd’s Model for the Independence of the Axiom of ChoiceMathworldPlanetmath, Providence: AMS.
  • 15 Blass, A. and Scedrov, A., 1992. CompletePlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath Topoi Representing Models of Set TheoryMathworldPlanetmath, Annals of Pure and Applied Logic , 57, no. 1, 1–26.
  • 16 Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5–29.
  • 17 Blute, R. and Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science
  • 18 Brown R. and T. Porter: 2003, Category theory and higher dimensional algebra: potential descriptive tools in neuroscience, In: Proceedings of the International Conference on Theoretical Neurobiology, Delhi, February 2003, edited by Nandini Singh, National Brain Research Centre, Conference Proceedings 1: 80-92.
  • 19 Brown, R., Hardie, K., Kamps, H. and T. Porter: 2002, The homotopy double groupoidPlanetmathPlanetmath of a Hausdorff space., Theory and Applications of Categories 10, 71-93.
  • 20 Brown, R. and Spencer, C.B.: 1976, Double groupoidsPlanetmathPlanetmathPlanetmath and crossed modules, Cah. Top. Géom. Diff. 17, 343-362.
  • 21 Brown R, Razak Salleh A (1999) Free crossed resolutions of groups and presentationsMathworldPlanetmathPlanetmath of modules of identitiesPlanetmathPlanetmathPlanetmathPlanetmath among relations. LMS J. Comput. Math., 2: 25–61.
  • 22 Buchsbaum, D. A.: 1955, Exact categories and duality., Trans. Amer. Math. Soc. 80: 1-34.
  • 23 Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes, Adv. in Math. 179, 291-317.
  • 24 Bunge, M., 1984, Toposes in Logic and Logic in Toposes, Topoi, 3, no. 1, 13-22.
  • 25 Bunge M, Lack S (2003) Van Kampen theorems for toposes. Adv Math, 179: 291-317.
  • 26 Ehresmann, C.: 1965, Catégories et Structures, Dunod, Paris.
  • 27 Ehresmann, C.: 1966, Trends Toward Unity in Mathematics., Cahiers de Topologie et Geometrie Differentielle 8: 1-7.

.1.2 b. Universal Algebra, Classes of Algebraic Structures and Homology; Abelian and Non-Abelian theories (http://planetmath.org/NonAbelianTheories); Algebraic Geometry and Noncommutative Geometry (http://planetmath.org/NoncommutativeGeometry)

.

References

  • 28 Brown, R., Higgins, P. J. and R. Sivera,: 2007, Non-AbelianMathworldPlanetmathPlanetmath Algebraic Topology, http://www.bangor.ac.uk/ mas010/nonab-t/partI010604.pdfvol.I pdf doc.; http://planetmath.org/?op=getobj&from=lec&id=75Review of Part I and full contents PDF doc.
  • 29 R. Brown. 2008. Higher Dimensional Algebra Preprint as pdf and ps docs. at arXiv:math/0212274v6 [math.AT]
  • 30 Brown, R., and Hardy, J.P.L.:1976, “Topological groupoidsPlanetmathPlanetmathPlanetmathPlanetmath I: universal constructions.”, Math. Nachr., 71: 273-286.
  • 31 Cartan, H. and Eilenberg, S. 1956. Homological Algebra, Princeton Univ. Press: Pinceton.
  • 32 Chevalley, C. 1946. The theory of Lie groups. Princeton University Press, Princeton NJ.
  • 33 M. Chaician and A. Demichev. 1996. Introduction to Quantum GroupsPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath, World Scientific .
  • 34 Cohen, P.M. 1965. Universal AlgebraMathworldPlanetmathPlanetmath, Harper and Row: New York, London and Tokyo.
  • 35 Connes A 1994. Noncommutative geometryPlanetmathPlanetmath. Academic Press: New York.
  • 36 Croisot, R. and Lesieur, L. 1963. Algèbre noethérienne non-commutative., Gauthier-Villard: Paris.
  • 37 Crole, R.L., 1994, Categories for Types, Cambridge: Cambridge University Press.
  • 38 Dieudonné, J. and Grothendieck, A., 1960, [1971], Éléments de Géométrie Algébrique, Berlin: Springer-Verlag.
  • 39 Dixmier, J., 1981, Von Neumann AlgebrasMathworldPlanetmathPlanetmathPlanetmath, Amsterdam: North-Holland Publishing Company. [First published in French in 1957: Les Algebres d’Operateurs dans l’Espace Hilbertien, Paris: Gauthier–Villars.]
  • 40 M. Durdevich : Geometry of quantum principal bundlesMathworldPlanetmath I, Commun. Math. Phys. 175 (3) (1996), 457–521.
  • 41 M. Durdevich : Geometry of quantum principal bundles II, Rev.Math. Phys. 9 (5) (1997), 531-607.
  • 42 Ehresmann, C.: 1952, Structures locales et structures infinitésimales, C.R.A.S. Paris 274: 587-589.
  • 43 Ehresmann, C.: 1959, Catégories topologiques et catégories différentiables, Coll. Géom. Diff. Glob. Bruxelles, pp.137-150.
  • 44 Ehresmann, C.:1963, Catégories doubles des quintettes: applications covariantes , C.R.A.S. Paris, 256: 1891–1894.
  • 45 Ehresmann, C.: 1984, Oeuvres complètes et commentées: Amiens, 1980-84, edited and commented by Andrée Ehresmann.
  • 46 Eilenberg, S. and S. Mac Lane.: 1942, Natural Isomorphisms in Group Theory., American Mathematical Society 43: 757-831.
  • 47 Eilenberg, S. and S. Mac Lane: 1945, The General Theory of Natural Equivalences, Transactions of the American Mathematical Society 58: 231-294.
  • 48 Eilenberg, S. & Cartan, H., 1956, Homological Algebra, Princeton: Princeton University Press.
  • 49 Eilenberg, S. & MacLane, S., 1942, Group ExtensionsMathworldPlanetmath and HomologyMathworldPlanetmathPlanetmath, Annals of Mathematics, 43, 757–831.
  • 50 Eilenberg, S. & Steenrod, N., 1952, Foundations of Algebraic Topology, Princeton: Princeton University Press.
  • 51 Eilenberg, S.: 1960. Abstract description of some basic functorsMathworldPlanetmath., J. Indian Math.Soc., 24 :221-234.
  • 52 S.Eilenberg. Relations between Homology and Homotopy GroupsMathworldPlanetmath. Proc.Natl.Acad.Sci.USA (1966),v:10–14.
  • 53 Ellerman, D., 1988, Category Theory and Concrete UniversalsPlanetmathPlanetmathPlanetmath, Synthese, 28, 409–429.
  • 54 Ezawa,Z.F., G. Tsitsishvilli and K. Hasebe : Noncommutative geometry, extended W∞ algebra and Grassmannian solitons in multicomponent Hall systems, (at arXiv:hep–th/0209198).
  • 55 Freyd, P., 2002, Cartesian Logic, Theoretical Computer Science, 278, no. 1–2, 3–21.
  • 56 Freyd, P., Friedman, H. & Scedrov, A., 1987, Lindembaum Algebras of Intuitionistic Theories and Free Categories, Annals of Pure and Applied Logic, 35, 2, 167–172.
  • 57 Gablot, R. 1971. Sur deux classes de catégories de Grothendieck. Thesis, Univ. de Lille.
  • 58 Gabriel, P.: 1962, Des catégories abéliennes, Bull. Soc. Math. France 90: 323-448.
  • 59 Gabriel, P. and M.Zisman:. 1967: Category of fractions and homotopy theory, Ergebnesse der math. Springer: Berlin.
  • 60 Gabriel, P. and N. Popescu: 1964, Caractérisation des catégories abéliennes avec générateurs et limites inductives. , CRAS Paris 258: 4188-4191.
  • 61 Galli, A. & Reyes, G. & Sagastume, M., 2000, Completeness Theorems via the Double Dual Functor, Studia Logica, 64, no. 1: 61–81.
  • 62 Gelfan’d, I. and Naimark, M., 1943, On the Imbedding of Normed RingsMathworldPlanetmath into the Ring of Operators in Hilbert SpaceMathworldPlanetmath, Recueil Mathématique [Matematicheskii Sbornik] Nouvelle Série, 12 [54]: 197–213. [Reprinted in C*–algebras: 1943–1993, in the series Contemporary Mathematics, 167, Providence, R.I.: American Mathematical Society, 1994.]
  • 63 Ghilardi, S. & Zawadowski, M., 2002, Sheaves, Games & Model Completions: A Categorical Approach to Nonclassical Propositional LogicsPlanetmathPlanetmath, Dordrecht: Kluwer.
  • 64 Ghilardi, S., 1989, PresheafMathworldPlanetmathPlanetmathPlanetmath Semantics and Independence Results for some Non-classical first-order logics, Archive for Mathematical Logic, 29, no. 2, 125–136.
  • 65 Goblot, R., 1968, Catégories modulaires , C. R. Acad. Sci. Paris, Série A., 267: 381–383.
  • 66 Goblot, R., 1971, Sur deux classes de catégories de Grothendieck, Thèse., Univ. Lille, 1971.
  • 67 Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and the foundations of mathematics, Amsterdam: Elsevier North-Holland Publ. Comp.
  • 68 Goldie, A. W., 1964, Localization in non-commutative noetherian ringsMathworldPlanetmath, J.Algebra, 1: 286-297.
  • 69 Godement,R. 1958. Théorie des faisceaux. Hermann: Paris.
  • 70 Gray, C. W.: 1965. Sheaves with values in a category.,TopologyMathworldPlanetmath, 3: 1-18.
  • 71 Grothendieck, A.: 1971, Revêtements Étales et Groupe Fondamental (SGA1), chapter VI: Catégories fibrées et descente, Lecture Notes in Math. 224, Springer–Verlag: Berlin.
  • 72 Grothendieck, A.: 1957, Sur quelque point d-algèbre homologique. , Tohoku Math. J., 9: 119-121.
  • 73 Grothendieck, A. and J. Dieudoné.: 1960, Eléments de geometrie algébrique., Publ. Inst. des Hautes Etudes de Science, 4.
  • 74 Grothendieck, A. et al., Séminaire de Géométrie Algébrique, Vol. 1–7, Berlin: Springer-Verlag.
  • 75 Hardie, K.A. K.H. Kamps and R.W. Kieboom, A homotopyMathworldPlanetmathPlanetmath 2-groupoid of a Hausdorff space, Applied Cat. Structures 8 (2000), 209-234.
  • 76 Hatcher, W. S., 1982, The Logical Foundations of Mathematics, Oxford: Pergamon Press.
  • 77 Heller, A. :1958, Homological algebra in Abelian categoriesMathworldPlanetmathPlanetmathPlanetmath., Ann. of Math. 68: 484-525.
  • 78 Heller, A. and K. A. Rowe.:1962, On the category of sheaves., Amer J. Math. 84: 205-216.
  • 79 Hellman, G., 2003, ”Does Category Theory Provide a Framework for Mathematical Structuralism?”, Philosophia Mathematica, 11, 2, 129–157.
  • 80 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.
  • 81 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.
  • 82 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.
  • 83 Higgins, P. J.: 2005, Categories and groupoidsPlanetmathPlanetmath, Van Nostrand Mathematical Studies: 32, (1971); Reprints in Theory and Applications of Categories, No. 7: 1-195.
  • 84 Higgins, Philip J. Thin elements and commutativePlanetmathPlanetmath shells in cubical ω-categories. Theory Appl. Categ. 14 (2005), No. 4, 60–74 (electronic). msc: 18D05.
  • 85 Hyland, J.M.E. & Robinson, E.P. & Rosolini, G., 1990, The Discrete Objects in the Effective Topos, Proceedings of the London Mathematical Society (3), 60, no. 1, 1–36.
  • 86 Hyland, J.M.E., 1982, The Effective Topos, Studies in Logic and the Foundations of Mathematics, 110, Amsterdam: North Holland, 165–216.
  • 87 Hyland, J. M..E., 1988, A Small Complete Category, Annals of Pure and Applied Logic, 40, no. 2, 135–165.
  • 88 Hyland, J. M .E., 1991, First Steps in Synthetic Domain Theory, Category Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer, 131-156.
  • 89 Hyland, J. M.E., 2002, Proof Theory in the Abstract, Annals of Pure and Applied Logic, 114, no. 1–3, 43–78.
  • 90 E.Hurewicz. CW Complexes., Trans AMS.1955.
  • 91 Jacobs, B., 1999, Categorical Logic and Type TheoryPlanetmathPlanetmath, Amsterdam: North Holland.
  • 92 Johnstone, P. T., 1977, Topos Theory, New York: Academic Press.
  • 93 Johnstone, P. T., 1979a, Conditions Related to De Morgan’s Law, Applications of Sheaves, Lecture Notes in Mathematics, 753, Berlin: Springer, 479–491.
  • 94 Johnstone, P. T., 1981, TychonoffPlanetmathPlanetmath’s Theorem without the Axiom of Choice, Fundamenta Mathematicae, 113, no. 1, 21–35.
  • 95 Johnstone, P. T., 1982, Stone Spaces, Cambridge:Cambridge University Press.
  • 96 Johnstone, P. T., 1985, How General is a Generalized Space?, Aspects of Topology, Cambridge: Cambridge University Press, 77–111.
  • 97 Joyal, A. & Moerdijk, I., 1995, Algebraic Set Theory, Cambridge: Cambridge University Press.
  • 98 Van Kampen, E. H.: 1933, On the Connection Between the Fundamental GroupsMathworldPlanetmathPlanetmath of some Related Spaces, Amer. J. Math. 55: 261-267
  • 99 Kan, D. M., 1958, Adjoint FunctorsMathworldPlanetmathPlanetmathPlanetmath, Transactions of the American Mathematical Society 87, 294-329.
  • 100 Kleisli, H.: 1962, Homotopy theory in Abelian categories.,Can. J. Math., 14: 139-169.
  • 101 Knight, J.T., 1970, On epimorphismsMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath of non-commutative rings., Proc. Cambridge Phil. Soc., 25: 266-271.
  • 102 Kock, A., 1981, Synthetic Differential Geometry, London Mathematical Society Lecture Note Series, 51, Cambridge: Cambridge University Press.
  • 103 S. Kobayashi and K. Nomizu : Foundations of Differential Geometry, Vol I., Wiley Interscience, New York–London 1963.
  • 104 H. Krips : Measurement in Quantum TheoryPlanetmathPlanetmath, The Stanford Encyclopedia of Philosophy (Winter 1999 Edition), Edward N. Zalta (ed.),
  • 105 Lam, T. Y., 1966, The category of noetherian modules, Proc. Natl. Acad. Sci. USA, 55: 1038-104.
  • 106 Lambek, J. & Scott, P.J., 1986, Introduction to Higher Order Categorical Logic, Cambridge: Cambridge University Press.
  • 107 Lambek, J., 1968, Deductive Systems and Categories I. Syntactic Calculus and Residuated Categories, Mathematical Systems Theory, 2, 287–318.
  • 108 Lambek, J., 1969, Deductive Systems and Categories II. Standard Constructions and Closed Categories, Category Theory, Homology Theory and their Applications I, Berlin: Springer, 76–122.
  • 109 Lambek, J., 1972, Deductive Systems and Categories III. Cartesian Closed Categories, Intuitionistic Propositional Calculus, and Combinatory LogicMathworldPlanetmath, Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, 274, Berlin: Springer, 57–82.
  • 110 Lambek, J., 1989A, On Some Connections Between Logic and Category Theory, Studia Logica, 48, 3, 269–278.
  • 111 Lambek, J., 1989B, On the Sheaf of Possible Worlds, Categorical Topology and its relation to AnalysisMathworldPlanetmath, Algebra and Combinatorics, Teaneck: World Scientific Publishing, 36–53.
  • 112 Lambek, J., 1994a, Some Aspects of Categorical Logic, in Logic, Methodology and Philosophy of Science IX, Studies in Logic and the Foundations of Mathematics 134, Amsterdam: North Holland, 69–89.
  • 113 Lambek, J., 2004, What is the world of Mathematics? Provinces of Logic Determined, Annals of Pure and Applied Logic, 126(1-3), 149–158.
  • 114 Lambek, J. and P. J. Scott. Introduction to higher order categorical logic. Cambridge University Press, 1986.
  • 115 E. C. Lance: Hilbert C*–Modules. London Math. Soc. Lect. Notes 210, Cambridge Univ. Press. 1995.
  • 116 Landry, E. & Marquis, J.-P., 2005, Categories in Context: Historical, Foundational and philosophical, Philosophia Mathematica, 13, 1–43.
  • 117 Landry, E., 1999, Category Theory: the Language of Mathematics, Philosophy of Science, 66, 3: supplement, S14–S27.
  • 118 Landsman, N. P.: 1998, Mathematical Topics between Classical and Quantum Mechanics, Springer Verlag: New York.
  • 119 Landsman, N. P. : CompactPlanetmathPlanetmath quantum groupoidsPlanetmathPlanetmath, (at arXiv:math–ph/9912006).
  • 120 La Palme Reyes, M., et. al., 1994, The non-Boolean Logic of Natural Language NegationMathworldPlanetmath, Philosophia Mathematica, 2, no. 1, 45–68.
  • 121 La Palme Reyes, M., et. al., 1999, Count Nouns, Mass Nouns, and their Transformations: a Unified Category-theoretic Semantics, LanguagePlanetmathPlanetmath, Logic and Concepts, Cambridge: MIT Press, 427–452.
  • 122 Lawvere, F. W., 1964, An Elementary Theory of the Category of Sets, Proceedings of the National Academy of Sciences U.S.A., 52, 1506–1511.
  • 123 Lawvere, F. W., 1965, Algebraic Theories, Algebraic Categories, and Algebraic Functors, Theory of Models, Amsterdam: North Holland, 413–418.
  • 124 Lawvere, F. W.: 1966, The Category of Categories as a Foundation for Mathematics., in Proc. Conf. Categorical Algebra- La Jolla., Eilenberg, S. et al., eds. Springer–Verlag: Berlin, Heidelberg and New York., pp. 1-20.
  • 125 Lawvere, F. W., 1969a, Diagonal Arguments and Cartesian Closed Categories, in Category Theory, Homology Theory, and their Applications II, Berlin: Springer, 134–145.
  • 126 Lawvere, F. W., 1969b, Adjointness in Foundations, Dialectica, 23: 281–295.
  • 127 Lawvere, F. W., 1970, Equality in Hyper doctrines and Comprehension Schema as an Adjoint Functor, Applications of Categorical Algebra, Providence: AMS, 1-14.
  • 128 Lawvere, F. W., 1971, QuantifiersMathworldPlanetmath and Sheaves, Actes du Congrés International des Mathématiciens, Tome 1, Paris: Gauthier-Villars, 329–334.
  • 129 Lawvere, F. W., 1972, Introduction, in Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, 274, Springer-Verlag, 1-12.
  • 130 Lawvere, F. W., 1975, Continuously Variable Sets: Algebraic Geometry = Geometric Logic, Proceedings of the Logic Colloquium, Bristol 1973, Amsterdam: North Holland, 135-153.
  • 131 Lawvere, F. W., 1976, Variable Quantities and Variable Structures, in Topoi, Algebra, Topology, and Category Theory, New York: Academic Press, 101–131.
  • 132 Lawvere, F. W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad. Sci. USA, Mathematics, 50: 869-872.
  • 133 Lawvere, F. W., 1992, Categories of Space and of Quantity, The Space of Mathematics, Foundations of Communication and Cognition, Berlin: De Gruyter, 14-30.
  • 134 Lawvere, F. W., 1994b, Tools for the Advancement of Objective Logic: Closed Categories and Toposes, The Logical Foundations of Cognition, Vancouver Studies in Cognitive Science, 4, Oxford: Oxford University Press, 43–56.
  • 135 Lawvere, F. W., 2000, Comments on the Development of Topos Theory, Development of Mathematics 1950-2000, Basel: Birkh’́auser, 715–734.
  • 136 Lawvere, F. W., 2002, Categorical Algebra for ContinuumMathworldPlanetmathPlanetmath Micro-Physics, Journal of Pure and Applied Algebra, 175, no. 1–3, 267–287.
  • 137 Lawvere, F. W., 2003, Foundations and Applications: Axiomatization and Education. New Programs and Open Problems in the Foundation of Mathematics, Bulletin of Symbolic Logic, 9, 2, 213–224.
  • 138 Leinster, T., 2002, A Survey of Definitions of n-categories, in Theory and Applications of Categories, (electronic), 10, 1–70.
  • 139 Li, M. and P. Vitanyi: 1997, An introduction to Kolmogorov Complexity and its Applications, Springer Verlag: New York.
  • 140 L’́ofgren, L.: 1968, An Axiomatic Explanation of Complete Self-Reproduction, Bulletin of Mathematical Biophysics, 30: 317-348
  • 141 Lubkin, S., 1960. Imbedding of abelian categories., Trans. Amer. Math. Soc., 97: 410-417.
  • 142 K. C. H. Mackenzie : Lie Groupoids and Lie Algebroids in Differential Geometry, LMS Lect. Notes 124, Cambridge University Press, 1987
  • 143 MacLane, S.: 1948. Groups, categories, and duality., Proc. Natl. Acad. Sci.U.S.A, 34: 263-267.
  • 144 MacLane, S., 1969, Foundations for Categories and Sets, in Category Theory, Homology Theory and their Applications II, Berlin: Springer, 146–164.
  • 145 MacLane, S., 1971, Categorical algebra and Set-Theoretic Foundations, in Axiomatic Set Theory, Providence: AMS, 231–240.
  • 146 MacLane, S., 1975, Sets, Topoi, and Internal Logic in Categories, Studies in Logic and the Foundations of Mathematics, 80, Amsterdam: North Holland, 119–134.
  • 147 MacLane, S., 1986, Mathematics, Form and Function, New York: Springer.
  • 148 MacLane, S., 1988, Concepts and Categories in Perspective, in A Century of Mathematics in America, Part I, Providence: AMS, 323–365.
  • 149 MacLane, S., 1989, The Development of Mathematical Ideas by Collision: the Case of Categories and Topos Theory, in Categorical Topology and its Relation to Analysis, Algebra and Combinatorics, Teaneck: World Scientific, 1–9.
  • 150 Maclane, S. and I. Moerdijk : Sheaves in Geometry and Logic – A first Introduction to Topos Theory, Springer Verlag, New York 1992.
  • 151 MacLane, S., 1950, Dualities for Groups, Bulletin of the American Mathematical Society, 56, 485-516.
  • 152 MacLane, S., 1996, Structure in Mathematics. Mathematical Structuralism., Philosophia Mathematica, 4, 2, 174-183.
  • 153 MacLane, S., 1997, Categories for the Working Mathematician, 2nd edition, New York: Springer-Verlag.
  • 154 Majid, S.: 1995, Foundations of Quantum Group Theory, Cambridge Univ. Press: Cambridge, UK.
  • 155 Majid, S.: 2002, A Quantum Groups Primer, Cambridge Univ.Press: Cambridge, UK.
  • 156 Makkai, M. & Paré, R., 1989, Accessible Categories: the Foundations of Categorical Model TheoryMathworldPlanetmath, Contemporary Mathematics, 104, Providence: AMS.
  • 157 Makkai, M., 1999, On Structuralism in Mathematics, in Language, Logic and Concepts, Cambridge: MIT Press, 43–66.
  • 158 Makkai, M. & Reyes, G., 1977, First-Order Categorical Logic, Springer Lecture Notes in Mathematics 611, New York: Springer.
  • 159 Makkei, M. & Reyes, G., 1995, Completeness Results for Intuitionistic and Modal Logic in a Categorical Setting, Annals of Pure and Applied Logic, 72, 1, 25–101.
  • 160 Marquis, J.-P., 1993, Russell’s Logicism and Categorical Logicisms, in Russell and Analytic Philosophy, A. D. Irvine & G. A. Wedekind, (eds.), Toronto, University of Toronto Press, 293–324.
  • 161 Marquis, J.-P., 1995, Category Theory and the Foundations of Mathematics: Philosophical Excavations., Synthese, 103, 421–447.
  • 162 Marquis, J.-P., 2006, Categories, Sets and the Nature of Mathematical Entities, in 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.
  • 163 May, J.P. 1999, A Concise Course in Algebraic Topology, The University of Chicago Press: Chicago.
  • 164 McCulloch, W. and W. Pitt.: 1943, A logical Calculus of Ideas Immanent in Nervous Activity., Bull. Math. Biophysics, 5: 115-133.
  • 165 Mc Larty, C., 1986, Left Exact Logic, Journal of Pure and Applied Algebra, 41, no. 1, 63-66.
  • 166 Mc Larty, C., 1991, Axiomatizing a Category of Categories, Journal of Symbolic Logic, 56, no. 4, 1243-1260.
  • 167 Mc Larty, C., 1992, Elementary Categories, Elementary Toposes, Oxford: Oxford University Press.
  • 168 Mc Larty, C., 1994, Category Theory in Real Time, Philosophia Mathematica, 2, no. 1, 36-44.
  • 169 Mc Larty, C., 2005, Learning from Questions on Categorical Foundations, Philosophia Mathematica, 13, 1, 44–60.
  • 170 Mitchell, B.: 1965, Theory of Categories, Academic Press:London.
  • 171 Mitchell, B.: 1964, The full imbedding theorem. Amer. J. Math. 86: 619-637.
  • 172 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.
  • 173 Moerdijk, I., 1998, Sets, Topoi and Intuitionism., Philosophia Mathematica, 6, no. 2, 169-177.
  • 174 I. Moerdijk : Classifying toposes and foliations, Ann. Inst. Fourier, Grenoble 41, 1 (1991) 189-209.
  • 175 I. Moerdijk : Introduction to the language of stacks and gerbes, (preprint at arXiv:math.AT/0212266) (2002).
  • 176 Morita, K. 1962. Category isomorphism and endomorphism ringsMathworldPlanetmath of modules, Trans. Amer. Math. Soc., 103: 451-469.
  • 177 Morita, K. , 1970. Localization in categories of modules. I., Math. Z., 114: 121-144.
  • 178 M. A. Mostow : The differentiable space structure of Milnor classifying spacesPlanetmathPlanetmath, simplicial complexesMathworldPlanetmath, and geometric realizations, J. Diff. Geom. 14 (1979) 255-293.
  • 179 Oberst, U.: 1969, Duality theory for Grothendieck categories., Bull. Amer. Math. Soc. 75: 1401-1408.
  • 180 Oort, F.: 1970. On the definition of an abelian category. Proc. Roy. Neth. Acad. Sci. 70: 13-02.
  • 181 Ore, O., 1931, Linear equations on non-commutative fields, Ann. Math. 32: 463-477.
  • 182 Plymen, R.J. and P. L. Robinson: 1994, Spinors in Hilbert Space, Cambridge Tracts in Math. 114, Cambridge Univ. Press, Cambridge.
  • 183 Popescu, N.: 1973, Abelian Categories with Applications to Rings and Modules. New York and London: Academic Press., 2nd edn. 1975. (English translation by I.C. Baianu).
  • 184 Pareigis, B., 1970, Categories and Functors, New York: Academic Press.
  • 185 Pedicchio, M. C. and Tholen, W., 2004, Categorical Foundations, Cambridge: Cambridge University Press.
  • 186 Peirce, B., 1991, Basic Category Theory for Computer Scientists, Cambridge: MIT Press.
  • 187 Pitts, A. M., 1989, Conceptual Completeness for First-order Intuitionistic LogicMathworldPlanetmath: an Application of Categorical Logic, Annals of Pure and Applied Logic, 41, no. 1, 33–81.
  • 188 Pitts, A. M., 2000, Categorical Logic, in Handbook of Logic in Computer Science, Vol.5, Oxford: Oxford Unversity Press, 39-128.
  • 189 Plotkin, B., 2000, Algebra, Categories and Databases, in Handbook of Algebra, Vol. 2, Amsterdam: Elsevier, 79–148.
  • 190 Pradines, J.: 1966, Théorie de Lie pour les groupoides différentiable, relation entre propriétes locales et globales, C. R. Acad Sci. Paris Sér. A 268: 907-910.
  • 191 Raptis, I.: 2003, Algebraic quantisation of causal sets, Int. Jour. Theor. Phys. 39: 1233.
  • 192 Reyes, G. & Zolfaghari, H., 1991, Topos-theoretic Approaches to Modality,in Category Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer, 359–378.
  • 193 Reyes, G. & Zolfaghari, H., 1996, Bi-Heyting Algebras, Toposes and Modalities, in Journal of Philosophical Logic, 25, no. 1, 25-43.
  • 194 Reyes, G., 1974, From Sheaves to Logic, in Studies in Algebraic Logic, A. Daigneault, ed., Providence: AMS.
  • 195 M. A. Rieffel : Group C*-algebras as compact quantum metric spaces, Documenta Math. 7 (2002), 605-651.
  • 196 Roberts, J. E.: 2004, More lectures on algebraic quantum field theory, in A. Connes, et al. Noncommutative Geometry, Springer: Berlin and New York.
  • 197 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.
  • 198 Rosen, R.: 1958b, The Representation of Biological Systems from the Standpoint of the Theory of Categories., Bulletin of Mathematical Biophysics 20: 317-341.
  • 199 G. C. Rota : On the foundation of combinatorial theory, I. The theory of Möbius functions, Zetschrif f’́ur Wahrscheinlichkeitstheorie 2 (1968), 340.
  • 200 Scott, P. J., 2000, Some Aspects of Categories in Computer Science, Handbook of Algebra, Vol. 2, Amsterdam: North Holland, 3–77.
  • 201 Shapiro, S., 2005, Categories, Structures and the Frege-Hilbert Controversy: the Status of MetamathematicsMathworldPlanetmathPlanetmathPlanetmath, Philosophia Mathematica, 13, 1, 61–77.
  • 202 Sorkin, R.D.: 1991, Finitary substitute for continuousPlanetmathPlanetmath topology, Int. J. Theor. Phys. 30 No. 7.: 923–947.
  • 203 Spanier, E. H.: 1966, Algebraic Topology, McGraw Hill: New York.
  • 204 Szabo, R. J.: 2003, Quantum field theory on non-commutative spaces, Phys. Rep. 378: 207–209.
  • 205 Thom, R.: 1980, Modèles mathématiques de la morphogénèse, Paris, Bourgeois.
  • 206 Taylor, P., 1996, Intuitionistic sets and OrdinalsMathworldPlanetmathPlanetmath, Journal of Symbolic Logic, 61, 705–744.
  • 207 Taylor, P., 1999, Practical Foundations of Mathematics, Cambridge: Cambridge University Press.
  • 208 Tierney, M., 1972, Sheaf Theory and the Continuum Hypothesis, Toposes, Algebraic Geometry and Logic.
  • 209 Van der Hoeven, G. and Moerdijk, I., 1984a, Sheaf Models for Choice Sequences, Annals of Pure and Applied Logic, 27, no. 1, 63–107.
  • 210 Várilly, J. C.: 1997, An introduction to noncommutative geometry. (at arXiv:physics/9709045)
  • 211 Weinstein, A.: 1996, Groupoids : unifying internal and external symmetryPlanetmathPlanetmath, Notices of the Amer. Math. Soc. 43: 744–752.
  • 212 Wess J. and J. Bagger: 1983, Supersymmetry and Supergravity, Princeton University Press: Princeton, NJ.
  • 213 Whitehead, J. H. C.: 1941, On adding relations to homotopy groups, Annals of Math. 42 (2): 409–428.
  • 214 Wood, R.J., 2004, Ordered Sets via Adjunctions, in Categorical Foundations, M. C. Pedicchio and W. Tholen, eds., Cambridge: Cambridge University Press.
Title bibliography for axiomatics and mathematics foundations in categories
Canonical name BibliographyForAxiomaticsAndMathematicsFoundationsInCategories
Date of creation 2013-03-22 18:19:31
Last modified on 2013-03-22 18:19:31
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 42
Author bci1 (20947)
Entry type Bibliography
Classification msc 55U99
Classification msc 03B50
Classification msc 18A05
Classification msc 18-00
Classification msc 03-00
Classification msc 00A15
Synonym metamathematics
Synonym mathematical foundations
Synonym axiomatics and formal logics
Related topic BibliographyForMathematicalPhysicsFoundationsAxiomaticsAndCategories
Related topic NonAbelianTheories
Related topic TopicEntryOnMiscellaneousMathematics