bibliography in algebraic topology,categories and QAT

Primary tabs

bibliography in algebraic topology,categories and QAT

This is an extensive, but not intended to be comprehensive, list of relevant, selected references for several areas of both abstract and applied mathematics. A more extensive bibliography on category theory can be found on the web at: Plato, Stanford Encyclopedia of Philosophy web site.

0.1 Literature for the following areas of mathematics:

Algebraic topology,
Theory of categories, functors and natural transformations,
Quantum algebraic topology,
N-logic algebraic categories,
Topoi and categorical ontology

References

1 Ad‘amek, J.. et al., Locally Presentable and Accessible Categories., Cambridge: Cambridge University Press (1994).
2 Alfsen, E.M. and F. W. Schultz: Geometry of State Spaces of Operator Algebras, Birkh'́auser, Boston–Basel–Berlin (2003).
3 Atiyah, M.F. 1956. On the Krull-Schmidt theorem with applications to sheaves. Bull. Soc. Math. France, 84: 307–317.
4 Auslander, M. 1965. Coherent Functors. Proc. Conf. Cat. Algebra, La Jolla, 189–231.
5 Awodey, S. & Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168–1182.
6 Awodey, S. & Reck, E. R., 2002, Completeness and Categoricity I. Nineteen-Century Axiomatics to Twentieth-Century Metalogic., History and Philosophy of Logic, 23, 1, 1–30.
7 Awodey, S. & Reck, E. R., 2002, Completeness and Categoricity II. Twentieth-Century Metalogic to Twenty-first-Century Semantics, History and Philosophy of Logic, 23, 2, 77-94.
8 Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective, Philosophia Mathematica, 3, 209-237.
9 Awodey, S., 2004, An Answer to Hellman’s Question: Does Category Theory Provide a Framework for Mathematical Structuralism., Philosophia Mathematica, 12, 54-64.
10 Awodey, S., 2006, Category Theory, Oxford: Clarendon Press.
11 Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes., Advances in Mathematics, 135, 145–206.
12 Baez, J. and Dolan, J., 1998b, “Categorification”, Higher Category Theory, Contemporary Mathematics, 230, Providence: AMS, 1-36.
13 Baez, J. and Dolan, J., 2001, “From Finite Sets to Feynman Diagrams”, Mathematics Unlimited – 2001 and Beyond, Berlin: Springer, 29-50.
14 Baez, J., 1997, “An Introduction to n-Categories”, Category Theory and Computer Science, Lecture Notes in Computer Science, 1290, Berlin: Springer-Verlag, 1–33.
15 Baianu, I.C. and M. Marinescu: 1968, Organismic Supercategories: Towards a Unitary Theory of Systems. Bulletin of Mathematical Biophysics 30, 148-159.
16 Baianu, I.C.: 1970, Organismic Supercategories: II. On Multistable Systems. Bulletin of Mathematical Biophysics, 32: 539-561.
17 Baianu, I.C.: 1971a, Organismic Supercategories and Qualitative Dynamics of Systems. Ibid., 33 (3), 339–354. First formal definition of quantum automata and quantum computing.
18 Baianu, I.C.: 1971b, Categories, Functors and Quantum Algebraic Computations, in P. Suppes (ed.), Proceed. Fourth Intl. Congress Logic-Mathematics-Philosophy of Science, September 1–4, 1971, Bucharest.
19 Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems. Bulletin of Mathematical Biophysics, 35(4), 475–486.
20 Baianu, I.C.: 1973, Some Algebraic Properties of (M,R) – Systems. Bulletin of Mathematical Biophysics 35, 213-217.
21 Baianu, I.C. and M. Marinescu: 1974, On A Functorial Construction of (M,R)– Systems. Revue Roumaine de Mathematiques Pures et Appliquees 19: 388-391.
22 Baianu, I.C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory. Bulletin of Mathematical Biology, 39: 249-258.
23 Baianu, I.C.: 1980a, Natural Transformations of Organismic Structures., Bulletin of Mathematical Biology,42: 431-446.
24 Baianu, I. C.: 1983, Natural Transformation Models in Molecular Biology., in Proceedings of the SIAM Natl. Meet., Denver,CO.; Eprint at cogprints.org/3675
25 Baianu, I.C.: 1984, A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Networks, FASEB Proceedings 43, 917.
26 Baianu, I. C.: 1986–1987a, Computer Models and Automata Theory in Biology and Medicine., in M. Witten (ed.), Mathematical Models in Medicine, vol. 7., Ch.11 Pergamon Press, New York, 1513 -1577; URLs: CERN Preprint No. EXT-2004-072 , and html Abstract.
27 Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures, in Proceed. Relational Biology Symp. Argentina; CERN Preprint No.EXT-2004-067 .
28 Baianu, I.C.: 2004a. Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models (2004). Eprint: w. Cogprints at Sussex Univ.
29 Baianu, I.C.: 2004b Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamics). CERN EXT-2004-059,Health Physics and Radiation Effects , (June 29, 2004).
30 Baianu, I. C., Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum Automata and N-Valued Łukasiewicz Algebras in Relation to Dynamic Bionetworks, (M,R)–Systems and Their Higher Dimensional Algebra, Abstract and Preprint of Report.
31 Baianu, I.C.: 2004a, Quantum Nano–Automata (QNA): Microphysical Measurements with Microphysical QNA Instruments, CERN Preprint EXT–2004–125.
32 Baianu, I. C.: 2004b, Quantum Interactomics and Cancer Mechanisms, Preprint 00001978 .
33 Baianu, I. C.: 2006, Robert Rosen’s Work and Complex Systems Biology, Axiomathes 16(1–2):25–34.
34 Baianu, I. C., Brown, R. and J. F. Glazebrook: 2006, Quantum Algebraic Topology and Field Theories. Preprint
35 Baianu, I.C.: 2008, Translational Genomics and Human Cancer Interactomics, (invited Review, submitted in November 2007 to Translational Oncogenomics).
36 Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006b, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., Axiomathes, 16 Nos. 1–2: 65–122.
37 Baianu, I.C., R. Brown and J.F. Glazebrook. : 2007a, Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness, Axiomathes, 17: 35-168.
38 Baianu, I.C., R. Brown and J. F. Glazebrook: 2007b, A Non-Abelian, Categorical Ontology of Spacetimes and Quantum Gravity, Axiomathes, 17: 169-225.
39 Baianu, I.C. et al. Quantum Algebra and Symmetries. PediaPress:Mainz, Germany, 1,112 pages, volumes I-III, Second edition. PM Books: “Quantum Algebra and Symmetries”
40 M. Barr and C. Wells. Toposes, Triples and Theories. Montreal: McGill University, 2000.
41 Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.
42 Barr, M. & Wells, C., 1999, Category Theory for Computing Science, Montreal: CRM.
43 Batanin, M., 1998, Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories”, Advances in Mathematics, 136, 39–103.
44 Bell, J. L., 1981, Category Theory and the Foundations of Mathematics, British Journal for the Philosophy of Science, 32, 349–358.
45 Bell, J. L., 1982, Categories, Toposes and Sets, Synthese,51, 3, 293–337.
46 Bell, J. L., 1986, From Absolute to Local Mathematics, Synthese, 69, 3, 409–426.
47 Bell, J. L., 1988, Toposes and Local Set Theories: An Introduction, Oxford: Oxford University Press.
48 Birkoff, G. and Mac Lane, S., 1999, Algebra, 3rd ed., Providence: AMS.
49 Biss, D.K., 2003, Which Functor is the Projective Line?, American Mathematical Monthly, 110, 7, 574–592.
50 Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111–140.
51 Blass, A. and Scedrov, A., 1989, Freyd’s Model for the Independence of the Axiom of Choice, Providence: AMS.
52 Blass, A. and Scedrov, A., 1992, Complete Topoi Representing Models of Set Theory, Annals of Pure and Applied Logic , 57, no. 1, 1-26.
53 Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5-29.
54 Blute, R. & Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science
55 Borceux, F.: 1994, Handbook of Categorical Algebra, vols: 1–3, in Encyclopedia of Mathematics and its Applications 50 to 52, Cambridge University Press.
56 Bourbaki, N. 1961 and 1964: Algèbre commutative., in Éléments de Mathématique., Chs. 1–6., Hermann: Paris.
57 R. Brown: Topology and Groupoids, BookSurge LLC (2006).
58 Brown, R. and G. Janelidze: 2004, Galois theory and a new homotopy double groupoid of a map of spaces, Applied Categorical Structures 12: 63-80.
59 Brown, R., Higgins, P. J. and R. Sivera,: 2007a, Non-Abelian Algebraic Topology, in preparation.
http://www.bangor.ac.uk/ mas010/nonab-a-t.html ;
http://www.bangor.ac.uk/ mas010/nonab-t/partI010604.pdf
60 Brown, R., Glazebrook, J. F. and I.C. Baianu.: 2007b, A Conceptual, Categorical and Higher Dimensional Algebra Framework of Universal Ontology and the Theory of Levels for Highly Complex Structures and Dynamics., Axiomathes (17): 321–379.
61 Brown, R., Paton, R. and T. Porter.: 2004, Categorical language and hierarchical models for cell systems, in Computation in Cells and Tissues - Perspectives and Tools of Thought, Paton, R.; Bolouri, H.; Holcombe, M.; Parish, J.H.; Tateson, R. (Eds.) Natural Computing Series, Springer Verlag, 289-303.
62 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.
63 Brown, R., Hardie, K., Kamps, H. and T. Porter: 2002, The homotopy double groupoid of a Hausdorff space., Theory and Applications of Categories 10, 71-93.
64 Brown, R., and Hardy, J.P.L.:1976, Topological groupoids I: universal constructions, Math. Nachr., 71: 273-286.
65 Brown, R. and T. Porter: 2006, Category Theory: an abstract setting for analogy and comparison, In: What is Category Theory?, Advanced Studies in Mathematics and Logic, Polimetrica Publisher, Italy, (2006) 257-274.
66 Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, Cah. Top. Géom. Diff. 17, 343-362.
67 Brown R, and Porter T (2006) Category theory: an abstract setting for analogy and comparison. In: What is category theory? Advanced studies in mathematics and logic. Polimetrica Publisher, Italy, pp. 257-274.
68 Brown R, Razak Salleh A (1999) Free crossed resolutions of groups and presentations of modules of identities among relations. LMS J. Comput. Math., 2: 25–61.
69 Buchsbaum, D. A.: 1955, Exact categories and duality., Trans. Amer. Math. Soc. 80: 1-34.
70 Buchsbaum, D. A.: 1969, A note on homology in categories., Ann. of Math. 69: 66-74.
71 Bucur, I. (1965). Homological Algebra. (orig. title: “Algebra Omologica”) Ed. Didactica si Pedagogica: Bucharest.
72 Bucur, I., and Deleanu A. (1968). Introduction to the Theory of Categories and Functors. J.Wiley and Sons: London
73 Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes, Adv. in Math. 179, 291-317.
74 Bunge, M., 1974, ”Topos Theory and Souslin’s Hypothesis”, Journal of Pure and Applied Algebra, 4, 159-187.
75 Bunge, M., 1984, ”Toposes in Logic and Logic in Toposes”, Topoi, 3, no. 1, 13-22.
76 Bunge M, Lack S (2003) Van Kampen theorems for toposes. Adv Math, 179: 291-317.
77 Butterfield J., Isham C.J. (2001) Spacetime and the philosophical challenges of quantum gravity. In: Callender C, Hugget N (eds) Physics meets philosophy at the Planck scale. Cambridge University Press, pp 33-89.
78 Butterfield J., Isham C.J. 1998, 1999, 2000-2002, A topos perspective on the Kochen-Specker theorem I-IV, Int J Theor Phys 37(11):2669-2733; 38(3):827-859; 39(6):1413-1436; 41(4): 613-639.
79 Cartan, H. and Eilenberg, S. 1956. Homological Algebra, Princeton Univ. Press: Pinceton.
80 M. Chaician and A. Demichev. 1996. Introduction to Quantum Groups, World Scientific .
81 Chevalley, C. 1946. The theory of Lie groups. Princeton University Press, Princeton NJ
82 Cohen, P.M. 1965. Universal Algebra, Harper and Row: New York, london and Tokyo.
83 Comoroshan S, and Baianu I.C. 1969. Abstract representations of biological systems in organismic supercategories: II. Limits and colimits.Bull Math Biophys 31: 84-93.
84 M. Crainic and R. Fernandes.2003. Integrability of Lie brackets, Ann.of Math. 157: 575-620.
85 Connes A 1994. Noncommutative geometry. Academic Press: New York.
86 Croisot, R. and Lesieur, L. 1963. Algèbre noethérienne non-commutative., Gauthier-Villard: Paris.
87 Crole, R.L., 1994, Categories for Types, Cambridge: Cambridge University Press.
88 Couture, J. & Lambek, J., 1991, Philosophical Reflections on the Foundations of Mathematics, Erkenntnis, 34, 2, 187–209.
89 DieudonnéJ. & Grothendieck, A., 1960, [1971], Éléments de Géométrie Algébrique, Berlin: Springer-Verlag.
90 Dirac, P. A. M., 1930, The Principles of Quantum Mechanics, Oxford: Clarendon Press.
91 Dirac, P. A. M., 1933, The Lagrangian in Quantum Mechanics, Physikalische Zeitschrift der Sowietunion, 3: 64-72.
92 Dirac, P. A. M.,, 1943, Quantum Electrodynamics, Communications of the Dublin Institute for Advanced Studies, A1: 1-36.
93 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.]
94 M. Durdevich : Geometry of quantum principal bundles I, Commun. Math. Phys. 175 (3) (1996), 457–521.
95 M. Durdevich : Geometry of quantum principal bundles II, Rev. Math. Phys. 9 (5) (1997), 531–607.
96 Ehresmann, C.: 1965, Catégories et Structures, Dunod, Paris.
97 Ehresmann, C.: 1966, Trends Toward Unity in Mathematics., Cahiers de Topologie et Geometrie Differentielle 8: 1-7.
98 Ehresmann, C.: 1952, Structures locales et structures infinitésimales, C.R.A.S. Paris 274: 587-589.
99 Ehresmann, C.: 1959, Catégories topologiques et catégories différentiables, Coll. Géom. Diff. Glob. Bruxelles, pp.137-150.
100 Ehresmann, C.:1963, Catégories doubles des quintettes: applications covariantes , C.R.A.S. Paris, 256: 1891–1894.
101 Ehresmann, A. C. & Vanbremeersch, J-P., 1987, ”Hierarchical Evolutive Systems: a Mathematical Model for Complex Systems”, Bulletin of Mathematical Biology, 49, no. 1, 13–50.
102 Ehresmann, C.: 1984, Oeuvres complètes et commentées: Amiens, 1980-84, edited and commented by Andrée Ehresmann.
103 Ehresmann, A. C. and J.-P. Vanbremersch: 1987, Hierarchical Evolutive Systems: A mathematical model for complex systems, Bull. of Math. Biol. 49 (1): 13-50.
104 Ehresmann, A. C. and J.-P. Vanbremersch: 2006, The Memory Evolutive Systems as a model of Rosen’s Organisms, Axiomathes 16 (1–2): 13-50.
105 Eilenberg, S. and S. Mac Lane.: 1942, Natural Isomorphisms in Group Theory., American Mathematical Society 43: 757-831.
106 Eilenberg, S. and S. Mac Lane: 1945, The General Theory of Natural Equivalences, Transactions of the American Mathematical Society 58: 231-294.
107 Eilenberg, S. & Cartan, H., 1956, Homological Algebra, Princeton: Princeton University Press.
108 Eilenberg, S. and MacLane, S., 1942, ”Group Extensions and Homology”, Annals of Mathematics, 43, 757–831.
109 S. Eilenberg and S. MacLane.1945. Relations between homology and homotopy groups of spaces. Ann. of Math., 46:480–509.
110 Eilenberg, S. and S. MacLane. 1950. Relations between homology and homotopy groups of spaces. II, Annals of Mathematics , 51: 514–533.
111 Eilenberg, S. and Steenrod, N., 1952, Foundations of Algebraic Topology, Princeton: Princeton University Press.
112 Eilenberg, S.: 1960. Abstract description of some basic functors., J. Indian Math.Soc., 24 :221-234.
113 Eilenberg, S. and S. Mac Lane. 1966. Relations between Homology and Homotopy Groups Proceed. Natl. Acad. Sci. (USA), Volume 29, Issue 5, pp. 155–158.
114 Ellerman, D., 1988, ”Category Theory and Concrete Universals”, Synthese, 28, 409–429.
115 Z. F. Ezawa, G. Tsitsishvilli and K. Hasebe : Noncommutative geometry, extended $W_{{\infty}}$ algebra and Grassmannian solitons in multicomponent Hall systems, arXiv:hep–th/0209198.
116 Feferman, S., 1977, “Categorical Foundations and Foundations of Category Theory”, Logic, Foundations of Mathematics and Computability, R. Butts (ed.), Reidel, 149–169.
117 Fell, J. M. G., 1960. “The Dual Spaces of C*–Algebras”, Transactions of the American Mathematical Society, 94: 365–403.
118 Feynman, R. P., 1948, “A Space–Time Approach to Non–Relativistic Quantum Mechanics.”, Reviews of Modern Physics, 20: 367—387. [It is reprinted in (Schwinger 1958).]
119 Freyd, P., 1960. Functor Theory (Dissertation). Princeton University, Princeton, New Jersey.
120 Freyd, P., 1963, Relative homological algebra made absolute. , Proc. Natl. Acad. USA, 49:19-20.
121 Freyd, P., 1964, Abelian Categories. An Introduction to the Theory of Functors, New York and London: Harper and Row.
122 Freyd, P., 1965, The Theories of Functors and Models., Theories of Models, Amsterdam: North Holland, 107–120.
123 Freyd, P., 1966, Algebra-valued Functors in general categories and tensor product in particular., Colloq. Mat. 14: 89–105.
124 Freyd, P., 1972, Aspects of Topoi,Bulletin of the Australian Mathematical Society, 7: 1–76.
125 Freyd, P., 1980, “The Axiom of Choice”, Journal of Pure and Applied Algebra, 19, 103–125.
126 Freyd, P., 1987, “Choice and Well-Ordering”, Annals of Pure and Applied Logic, 35, 2, 149–166.
127 Freyd, P., 1990, Categories, Allegories, Amsterdam: North Holland.
128 Freyd, P., 2002, “Cartesian Logic”, Theoretical Computer Science, 278, no. 1–2, 3–21.
129 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.
130 Gablot, R. 1971. Sur deux classes de catégories de Grothendieck. Thesis.. Univ. de Lille.
131 Gabriel, P.: 1962, Des catégories abéliennes, Bull. Soc. Math. France 90: 323-448.
132 Gabriel, P. and M.Zisman:. 1967: Category of fractions and homotopy theory, Ergebnesse der math. Springer: Berlin.
133 Gabriel, P. and N. Popescu: 1964, Caractérisation des catégories abéliennes avec générateurs et limites inductives. , CRAS Paris 258: 4188-4191.
134 Galli, A. & Reyes, G. & Sagastume, M., 2000, ”Completeness Theorems via the Double Dual Functor”, Studia Logical, 64, no. 1, 61–81.
135 Gelfan’d, I. and Naimark, M., 1943, “On the Imbedding of Normed Rings into the Ring of Operators in Hilbert Space, 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.]
136 Georgescu, G. and C. Vraciu 1970. “On the Characterization of Łukasiewicz Algebras.” J Algebra, 16 (4), 486-495.
137 Ghilardi, S. & Zawadowski, M., 2002, “Sheaves, Games & Model Completions: A Categorical Approach to Nonclassical Porpositional Logics”, Dordrecht: Kluwer.
138 Ghilardi, S., 1989, “Presheaf Semantics and Independence Results for some Non-classical first-order logics.”, Archive for Mathematical Logic, 29, no. 2, 125–136.
139 Goblot, R., 1968, Catégories modulaires , C. R. Acad. Sci. Paris, Série A., 267: 381–383.
140 Goblot, R., 1971, Sur deux classes de catégories de Grothendieck, Thèse., Univ. Lille, 1971.
141 Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and the foundations of mathematics, Amsterdam: Elsevier North-Holland Publ. Comp.
142 Goldie, A. W., 1964, Localization in non-commutative noetherian rings, J.Algebra, 1: 286-297.
143 Godement,R. 1958. Théorie des faisceaux. Hermann: Paris.
144 Gray, C. W.: 1965. Sheaves with values in a category.,Topology, 3: 1-18.
145 Grothendieck, A.: 1971, Revêtements Étales et Groupe Fondamental (SGA1), chapter VI: Catégories fibrées et descente, Lecture Notes in Math. 224, Springer–Verlag: Berlin.
146 Grothendieck, A.: 1957, Sur quelque point d-algébre homologique. , Tohoku Math. J., 9: 119-121.
147 Grothendieck, A. and J. Dieudoné.: 1960, Eléments de geometrie algébrique., Publ. Inst. des Hautes Etudes de Science, 4.
148 Grothendieck, A. et al., “Séminaire de Géométrie Algébrique.”, Vol. 1–7, Berlin: Springer-Verlag.
149 Grothendieck, A., 1957, “Sur Quelques Points d’algébre homologique.”, Tohoku Mathematics Journal, 9, 119–221.
150 Groups Authors: J. Faria Martins, Timothy Porter., On Yetter’s Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical $math.QA/0608484[abs,ps,pdf,other]$ .
151 Gruson, L, 1966, Complétion abélienne. Bull. Math.Soc. France, 90: 17-40.
152 K.A. Hardie, K.H. Kamps and R.W. Kieboom, A homotopy 2-groupoid of a Hausdorff space, Applied Cat. Structures 8 (2000), 209-234.
153 Hatcher, W. S., 1982, The Logical Foundations of Mathematics, Oxford: Pergamon Press.
154 Healy, M. J., 2000, “Category Theory Applied to Neural Modeling and Graphical Representations”, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks: IJCNN200, Como, vol. 3, M. Gori, S-I. Amari, C. L. Giles, V. Piuri, eds., IEEE Computer Science Press, 35–40.
155 Heller, A. :1958, Homological algebra in Abelian categories., Ann. of Math. 68: 484-525.
156 Heller, A. and K. A. Rowe.:1962, On the category of sheaves., Amer J. Math. 84: 205-216.
157 Hellman, G., 2003, “Does Category Theory Provide a Framework for Mathematical Structuralism?”, Philosophia Mathematica, 11, 2, 129–157.
158 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.
159 Hermida, C. & Makkai, M. & Power, J., 2001, “On Weak Higher-dimensional Categories 2”, Journal of Pure and Applied Algebra, 157, no. 2-3, 247–277.
160 Hermida, C. & Makkai, M. & Power, J., 2002, “On Weak Higher-dimensional Categories 3”, Journal of Pure and Applied Algebra, 166, no. 1-2, 83–104.
161 Higgins, P. J.: 2005, Categories and groupoids, Van Nostrand Mathematical Studies: 32, (1971); Reprints in Theory and Applications of Categories, No. 7: 1-195.
162 Higgins, Philip J. Thin elements and commutative shells in cubical $\omega$ -categories. Theory Appl. Categ. 14 (2005), No. 4, 60–74 (electronic). (Reviewer: Timothy Porter) 18D05.
163 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.
164 Hyland, J.M.E., 1982, “The Effective Topos”, Studies in Logic and the Foundations of Mathematics, 110, Amsterdam: North Holland, 165–216.
165 Hyland, J. M..E., 1988, “A Small Complete Category”, Annals of Pure and Applied Logic, 40, no. 2, 135–165.
166 Hyland, J. M .E., 1991, “First Steps in Synthetic Domain Theory.”, Category Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer, 131-156.
167 Hyland, J. M.E., 2002, “Proof Theory in the Abstract.”, Annals of Pure and Applied Logic, 114, no. 1–3, 43–78.
168 E.Hurewicz. CW Complexes.Trans AMS.1955.
169 Ionescu, Th., R. Parvan and I. Baianu, 1970, C. R. Acad. Sci. Paris, Série A., 269: 112-116, communiquée par Louis Néel.
170 C. J. Isham : A new approach to quantising space–time: I. quantising on a general category, Adv. Theor. Math. Phys. 7 (2003), 331–367.
171 Jacobs, B., 1999, Categorical Logic and Type Theory, Amsterdam: North Holland.
172 Johnstone, P. T., 1977, Topos Theory, New York: Academic Press.
173 Johnstone, P. T., 1979a, “Conditions Related to De Morgan’s Law.”, Applications of Sheaves, Lecture Notes in Mathematics, 753, Berlin: Springer, 479–491.
174 Johnstone, P.T., 1979b, “Another Condition Equivalent to De Morgan’s Law.”, Communications in Algebra, 7, no. 12, 1309–1312.
175 Johnstone, P. T., 1981, “Tychonoff’s Theorem without the Axiom of Choice.”, Fundamenta Mathematicae, 113, no. 1, 21–35.
176 Johnstone, P. T., 1982, “Stone Spaces.”, Cambridge:Cambridge University Press.
177 Johnstone, P. T., 1985, “How General is a Generalized Space?”, Aspects of Topology, Cambridge: Cambridge University Press, 77–111.
178 Johnstone, P. T., 2002a, Sketches of an Elephant: a Topos Theory Compendium. Vol. 1, Oxford Logic Guides, 43, Oxford: Oxford University Press.
179 Joyal, A. & Moerdijk, I., 1995, “Algebraic Set Theory.”, Cambridge: Cambridge University Press.
180 Van Kampen, E. H.: 1933, On the Connection Between the Fundamental Groups of some Related Spaces, Amer. J. Math. 55: 261-267
181 Kan, D. M., 1958, “Adjoint Functors.”, Transactions of the American Mathematical Society, 87, 294-329.
182 Kleisli, H.: 1962, Homotopy theory in Abelian categories.,Can. J. Math., 14: 139-169.
183 Knight, J.T., 1970, On epimorphisms of non-commutative rings., Proc. Cambridge Phil. Soc., 25: 266-271.
184 Kock, A., 1981, Synthetic Differential Geometry, London Mathematical Society Lecture Note Series, 51, Cambridge: Cambridge University Press.
185 S. Kobayashi and K. Nomizu : Foundations of Differential Geometry Vol I., Wiley Interscience, New York–London 1963.
186 H. Krips : Measurement in Quantum Theory, The Stanford Encyclopedia of Philosophy (Winter 1999 Edition), Edward N. Zalta (ed.), $URL=<http://plato.stanford.edu/archives/win1999/entries/qt--measurement/>$
187 Lam, T. Y., 1966, The category of noetherian modules, Proc. Natl. Acad. Sci. USA, 55: 1038-104.
188 Lambek, J. & Scott, P. J., 1981, “Intuitionistic Type Theory and Foundations”, Journal of Philosophical Logic, 10, 1, 101–115.
189 Lambek, J. & Scott, P.J., 1986, Introduction to Higher Order Categorical Logic, Cambridge: Cambridge University Press.
190 Lambek, J., 1968, “Deductive Systems and Categories I. Syntactic Calculus and Residuated Categories”, Mathematical Systems Theory, 2, 287–318.
191 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.
192 Lambek, J., 1972, “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.
193 Lambek, J., 1982, “The Influence of Heraclitus on Modern Mathematics.”, Scientific Philosophy Today, J. Agassi and R.S. Cohen, eds., Dordrecht, Reidel, 111–122.
194 Lambek, J., 1986, “Cartesian Closed Categories and Typed lambda calculi.”, Combinators and Functional Programming Languages, Lecture Notes in Computer Science, 242, Berlin: Springer, 136–175.
195 Lambek, J., 1989A, “On Some Connections Between Logic and Category Theory.”, Studia Logica, 48, 3, 269–278.
196 Lambek, J., 1989B, “On the Sheaf of Possible Worlds.”, Categorical Topology and its relation to Analysis, Algebra and Combinatorics, Teaneck: World Scientific Publishing, 36–53.
197 Lambek, J., 1994a, “Some Aspects of Categorical Logic.”, Logic, Methodology and Philosophy of Science IX, Studies in Logic and the Foundations of Mathematics 134, Amsterdam: North Holland, 69–89.
198 Lambek, J., 1994b, “What is a Deductive System?”, What is a Logical System?, Studies in Logic and Computation, 4, Oxford: Oxford University Press, 141–159.
199 Lambek, J., 2004, “What is the world of Mathematics? Provinces of Logic Determined.”, Annals of Pure and Applied Logic, 126(1-3), 149–158.
200 Lambek, J. and P. J. Scott. Introduction to higher order categorical logic. Cambridge University Press, 1986.
201 E. C. Lance : Hilbert C*–Modules. London Math. Soc. Lect. Notes 210, Cambridge Univ. Press. 1995.
202 Landry, E. & Marquis, J.-P., 2005, “Categories in Context: Historical, Foundational and philosophical”, Philosophia Mathematica, 13, 1–43.
203 Landry, E., 1999, “Category Theory: the Language of Mathematics.”, Philosophy of Science, 66, 3: supplement, S14–S27.
204 Landry, E., 2001, “Logicism, Structuralism and Objectivity.”, Topoi, 20, 1, 79–95.
205 Landsman, N. P.: 1998, Mathematical Topics between Classical and Quantum Mechanics, Springer Verlag: New York.
206 N. P. Landsman : Mathematical topics between classical and quantum mechanics. Springer Verlag, New York, 1998.
207 N. P. Landsman : Compact quantum groupoids, arXiv:math-ph/9912006
208 La Palme Reyes, M., et. al., 1994, “The non-Boolean Logic of Natural Language Negation.”, Philosophia Mathematica, 2, no. 1, 45–68.
209 La Palme Reyes, M., et. al., 1999, “Count Nouns, Mass Nouns, and their Transformations: a Unified Category-theoretic Semantics.”, Language, Logic and Concepts, Cambridge: MIT Press, 427–452.
210 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.
211 Lawvere, F. W., 1965, “Algebraic Theories, Algebraic Categories, and Algebraic Functors.”, Theory of Models, Amsterdam: North Holland, 413–418.
212 Lawvere, F. W., 1966, “The Category of Categories as a Foundation for Mathematics.”, Proceedings of the Conference on Categorical Algebra, La Jolla, New York: Springer-Verlag, 1–21.
213 Lawvere, F. W., 1969a, “Diagonal Arguments and Cartesian Closed Categories.”, Category Theory, Homology Theory, and their Applications II, Berlin: Springer, 134–145.
214 Lawvere, F. W., 1969b, “Adjointness in Foundations.”, Dialectica, 23, 281–295.
215 Lawvere, F. W., 1970, “Equality in Hyper doctrines and Comprehension Schema as an Adjoint Functor”, Applications of Categorical Algebra, Providence: AMS, 1-14.
216 Lawvere, F. W., 1971, “Quantifiers and Sheaves.”, Actes du Congrés International des Mathématiciens, Tome 1, Paris: Gauthier-Villars, 329–334.
217 Lawvere, F. W., 1975, Continuously Variable Sets: Algebraic Geometry = Geometric Logic., “Introduction”, In: Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, 274, Springer—erlag, 1-12. Lawvere, F. W., 1975, Proceedings of the Logic Colloquium Bristol, 1973, Amsterdam: North Holland, 135–153.
218 Lawvere, F. W., 1976, “Variable Quantities and Variable Structures in Topoi.”, Algebra, Topology, and Category Theory, New York: Academic Press, 101–131.
219 Lawvere, F. W. & Schanuel, S., 1997, Conceptual Mathematics: A First Introduction to Categories, Cambridge: Cambridge University Press.
220 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.
221 Lawvere, F. W.: 1963, Functorial Semantics of Algebraic Theories, Proc. Natl. Acad. Sci. USA, Mathematics, 50: 869-872.
222 Lawvere, F. W.: 1969, Closed Cartesian Categories., Lecture held as a guest of the Romanian Academy of Sciences, Bucharest.
223 Lawvere, F. W., 1992, “Categories of Space and of Quantity.”, The Space of Mathematics, Foundations of Communication and Cognition, Berlin: De Gruyter, 14–30.
224 Lawvere, F. W., 1994a, “Cohesive Toposes and Cantor’s lauter Ensein.”, Philosophia Mathematica, 2, 1, 5–15.
225 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.
226 Lawvere, H. W (ed.), 1995. Springer Lecture Notes in Mathematics 274,:13–42.
227 Lawvere, F. W., 2000, “Comments on the Development of Topos Theory.”, Development of Mathematics 1950-2000, Basel: Birkhäuser, 715–734.
228 Lawvere, F. W., 2002, “Categorical Algebra for Continuum Micro Physics.”, Journal of Pure and Applied Algebra, 175, no. 1–3, 267–287.
229 Lawvere, F. W. & Rosebrugh, R., 2003, Sets for Mathematics, Cambridge: Cambridge University Press.
230 Lawvere, F. W., 2003, “Foundations and Applications: Axiomatization and Education. New Programs and Open Problems in the Foundation of Mathematics.”, Bullentin of Symbolic Logic, 9, 2, 213–224.
231 Lawvere, F.W., 1963, “Functorial Semantics of Algebraic Theories.”, Proceedings of the National Academy of Sciences U.S.A., 50, 869–872.
232 Leinster, T., 2002, “A Survey of Definitions of $n$ -categories.”, Theory and Applications of Categories, (electronic), 10, 1–70.
233 Li, M. and P. Vitanyi: 1997, An introduction to Kolmogorov Complexity and its Applications, Springer Verlag: New York.
234 L'́ofgren, L.: 1968, “An Axiomatic Explanation of Complete Self-Reproduction.”, Bulletin of Mathematical Biophysics, 30: 317-348
235 Lubkin, S., 1960. “Imbedding of abelian categories.”, Trans. Amer. Math. Soc., 97: 410-417.
236 Luisi, P. L. and F. J. Varela: 1988, “Self-replicating micelles a chemical version of a minimal autopoietic system.”, Origins of Life and Evolution of Biospheres. 19(6):633–643.
237 K. C. H. Mackenzie: “Lie Groupoids and Lie Algebroids in Differential Geometry.”, LMS Lect. Notes 124, Cambridge University Press, 1987
238 MacLane, S.: 1948. Groups, categories, and duality., Proc. Natl. Acad. Sci.U.S.A, 34: 263-267.
239 MacLane, S., 1969, “Foundations for Categories and Sets.’, Category Theory, Homology Theory and their Applications II, Berlin: Springer, 146–164.
240 MacLane, S., 1969, “One Universe as a Foundation for Category Theory.”, Reports of the Midwest Category Seminar III, Berlin: Springer, 192–200.
241 MacLane, S., 1971, “Categorical algebra and Set-Theoretic Foundations”, Axiomatic Set Theory, Providence: AMS, 231–240.
242 MacLane, S., 1975, “Sets, Topoi, and Internal Logic in Categories.”, Studies in Logic and the Foundations of Mathematics, 80, Amsterdam: North Holland, 119–134.
243 MacLane, S., 1981, “Mathematical Models: a Sketch for the Philosophy of Mathematics.”, American Mathematical Monthly, 88, 7, 462–472.
244 MacLane, S. 1986. Mathematics, Form and Function, New York: Springer.
245 MacLane, S., 1988, “Concepts and Categories in Perspective”, A Century of Mathematics in America, Part I, Providence: AMS, 323–365.
246 MacLane, S., 1989, “The Development of Mathematical Ideas by Collision: the Case of Categories and Topos Theory.”, Categorical Topology and its Relation to Analysis, Algebra and Combinatorics, Teaneck: World Scientific, 1–9.
247 S. Maclane and I. Moerdijk. Sheaves in Geometry and Logic- A first Introduction to Topos Theory., Springer Verlag, New York, 1992.
248 MacLane, S., 1950, “Dualities for Groups”, Bulletin of the American Mathematical Society., 56, 485-516.
249 MacLane, S., 1996, Structure in Mathematics. Mathematical Structuralism., Philosophia Mathematica, 4, 2, 174-183.
250 MacLane, S., 1997, Categories for the Working Mathematician, 2nd edition, New York: Springer-Verlag.
251 MacLane, S., 1997, Categorical Foundations of the Protean Character of Mathematics., Philosophy of Mathematics Today, Dordrecht: Kluwer, 117–122.
252 MacLane, S., and I. Moerdijk. Sheaves and Geometry in Logic: A First Introduction to Topos Theory, Springer-Verlag, 1992.
253 Majid, S.: 1995, Foundations of Quantum Group Theory, Cambridge Univ. Press: Cambridge, UK.
254 Majid, S.: 2002, A Quantum Groups Primer, Cambridge Univ.Press: Cambridge, UK.
255 Makkai, M. & Paré, R., 1989, Accessible Categories: the Foundations of Categorical Model Theory, Contemporary Mathematics 104, Providence: AMS.
256 Makkai, M., 1998, Towards a Categorical Foundation of Mathematics, Lecture Notes in Logic, 11, Berlin: Springer, 153–190.
257 Makkai, M., 1999, “On Structuralism in Mathematics”, in Language, Logic and Concepts, Cambridge: MIT Press, 43–66.
258 Makkai, M. & Reyes, G., 1977, First-Order Categorical Logic, Springer Lecture Notes in Mathematics 611, New York: Springer.
259 Makkai, M., 1998, “Towards a Categorical Foundation of Mathematics.”, Lecture Notes in Logic, 11, Berlin: Springer, 153–190.
260 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.
261 Mallios, A. and I. Raptis: 2003, Finitary, Causal and Quantal Vacuum Einstein Gravity, Int. J. Theor. Phys. 42: 1479.
262 Manders, K.L.: 1982, On the space-time ontology of physical theories, Philosophy of Science 49 no. 4: 575–590.
263 Marquis, J.-P., 1993, “Russell’s Logicism and Categorical Logicisms”, Russell and Analytic Philosophy, A. D. Irvine & G. A. Wedekind, (eds.), Toronto, University of Toronto Press, 293–324.
264 Marquis, J.-P., 1995, Category Theory and the Foundations of Mathematics: Philosophical Excavations., Synthese, 103, 421–447.
265 Marquis, J.-P., 2000, “Three Kinds of Universals in Mathematics?”, Logical Consequence: Rival Approaches and New Studies in Exact Philosophy: Logic, Mathematics and Science, Vol. 2, Oxford: Hermes, 191–212.
266 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.
267 Martins, J. F and T. Porter: 2004, On Yetter’s Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical Groups, math.QA/0608484
268 Maturana, H. R. and F. J. Varela: 1980, Autopoiesis and Cognition-The Realization of the Living, Boston Studies in the Philosophy of Science Vol. 42, Reidel Pub. Co.: Dordrecht.
269 May, J.P. 1999, A Concise Course in Algebraic Topology, The University of Chicago Press: Chicago.
270 McCulloch, W. and W. Pitt.: 1943, A logical Calculus of Ideas Immanent in Nervous Activity., Bull. Math. Biophysics, 5: 115-133.
271 Mc Larty, C., 1986, Left Exact Logic, Journal of Pure and Applied Algebra, 41, no. 1, 63-66.
272 Mc Larty, C., 1991, “Axiomatizing a Category of Categories.”, Journal of Symbolic Logic, 56, no. 4, 1243-1260.
273 Mc Larty, C., 1992, “Elementary Categories, Elementary Toposes”, Oxford: Oxford University Press.
274 Mc Larty, C., 1994, “Category Theory in Real Time.”, Philosophia Mathematica, 2, no. 1, 36-44.
275 Mc Larty, C., 2004, “Exploring Categorical Structuralism”, Philosophia Mathematica, 12, 37-53.
276 Mc Larty, C., 2005, “Learning from Questions on Categorical Foundations”, Philosophia Mathematica, 13, 1, 44–60.
277 Misra, B., I. Prigogine and M. Courbage.: 1979, Lyaponouv variables: Entropy and measurement in quantum mechanics, Proc. Natl. Acad. Sci. USA 78 (10): 4768–4772.
278 Mitchell, B.: 1965, Theory of Categories, Academic Press:London.
279 Mitchell, B.: 1964, The full imbedding theorem. Amer. J. Math. 86: 619-637.
280 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.
281 Moerdijk, I., 1998, Sets, Topoi and Intuitionism., Philosophia Mathematica, 6, no. 2, 169-177.
282 I. Moerdijk : Classifying toposes and foliations, Ann. Inst. Fourier, Grenoble 41, 1 (1991) 189-209.
283 I. Moerdijk. Introduction to the language of stacks and gerbes, $arXiv:math.AT/0212266$ (2002).
284 Morita, K. 1962. “Category isomorphism and endomorphism rings of modules.”, Trans. Amer. Math. Soc., 103: 451-469.
285 Morita, K. 1970. “Localization in categories of modules. I.”, Math. Z., 114: 121-144.
286 M. A. Mostow. “The differentiable space structure of Milnor classifying spaces, simplicial complexes, and geometric realizations.”, J. Diff. Geom. 14 (1979) 255-293.
287 Oberst, U. 1969. “Duality theory for Grothendieck categories.”, Bull. Amer. Math. Soc. 75: 1401-1408.
288 Oort, F.: 1967. On the definition of an abelian category. Proceed. Kon. Acad. Wetensch., 70: 83 –92.
289 Ore, O., 1931, Linear equations on non-commutative fields, Ann. Math. 32: 463-477.
290 Penrose, R.: 1994, Shadows of the Mind, Oxford University Press: Oxford.
291 Plymen, R.J. and P. L. Robinson: 1994, Spinors in Hilbert Space, Cambridge Tracts in Math. 114, Cambridge Univ. Press, Cambridge.
292 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).
293 Pareigis, B., 1970, Categories and Functors, New York: Academic Press.
294 Pedicchio, M. C. & Tholen, W., 2004, Categorical Foundations, Cambridge: Cambridge University Press.
295 Peirce, B., 1991, Basic Category Theory for Computer Scientists, Cambridge: MIT Press.
296 Pitts, A. M., 1989, “Conceptual Completeness for First-order Intuitionistic Logic: an Application of Categorical Logic.”, Annals of Pure and Applied Logic, 41, no. 1, 33–81.
297 Pitts, A. M., 2000, “Categorical Logic”, Handbook of Logic in Computer Science, Vol.5, Oxford: Oxford Unversity Press, 39–128.
298 Plotkin, B., 2000, “Algebra, Categories and Databases”, Handbook of Algebra, Vol. 2, Amsterdam: Elsevier, 79–148.
299 Poli, R.: 2008, Ontology: The Categorical Stance, (in TAO1- Theory and Applications of Ontology: vol.1).
300 Poli, R. (with I.C. Baianu): 2008, Categorical Ontology: the theory of levels, (in TAO1- Theory and Applications of Ontology: vol.1), in press.
301 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).
302 Porter, T.: 2002, Geometric aspects of multiagent sytems, preprint University of Wales-Bangor.
303 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.
304 Pribram, K. H.: 1991, Brain and Perception: Holonomy and Structure in Figural processing, Lawrence Erlbaum Assoc.: Hillsdale.
305 Pribram, K. H.: 2000, Proposal for a quantum physical basis for selective learning, in (Farre, ed.) Proceedings ECHO IV 1-4.
306 Prigogine, I.: 1980, From Being to Becoming : Time and Complexity in the Physical Sciences, W. H. Freeman and Co.: San Francisco.
307 Raptis, I. and R. R. Zapatrin: 2000, Quantisation of discretized spacetimes and the correspondence principle, Int. Jour. Theor. Phys. 39: 1.
308 Raptis, I. 2003, Algebraic quantisation of causal sets, Int. Jour. Theor. Phys. 39: 1233.
309 I. Raptis. Quantum space–time as a quantum causal set, arXiv:gr–qc/0201004.
310 Rashevsky, N. 1965, The Representation of Organisms in Terms of Predicates, Bulletin of Mathematical Biophysics 27: 477-491.
311 Rashevsky, N. 1969, Outline of a Unified Approach to Physics, Biology and Sociology., Bulletin of Mathematical Biophysics 31: 159–198.
312 Reyes, G. & Zolfaghari, H., 1991, “Topos-theoretic Approaches to Modality.”, Category Theory (Como 1990), Lecture Notes in Mathematics, 1488, Berlin: Springer, 359–378.
313 Reyes, G. & Zolfaghari, H., 1996, “Bi-Heyting Algebras, Toposes and Modalities.”, Journal of Philosophical Logic, 25, no. 1, 25–43.
314 Reyes, G., 1974, “From Sheaves to Logic.”, in Studies in Algebraic Logic, A. Daigneault, ed., Providence: AMS.
315 Reyes, G., 1991, “A Topos-theoretic Approach to Reference and Modality”, Notre Dame Journal of Formal Logic, 32, no. 3, 359-391.
316 M. A. Rieffel : Group C*–algebras as compact quantum metric spaces, Documenta Math. 7 (2002), 605-651.
317 Roberts, J. E.: 2004, More lectures on algebraic quantum field theory, in A. Connes, et al. Noncommutative Geometry, Springer: Berlin and New York.
318 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.
319 Rosen, R.: 1985, Anticipatory Systems, Pergamon Press: New York.
320 Rosen, R.: 1958a, A Relational Theory of Biological Systems Bulletin of Mathematical Biophysics 20: 245-260.
321 Rosen, R.: 1958b, The Representation of Biological Systems from the Standpoint of the Theory of Categories., Bulletin of Mathematical Biophysics 20: 317-341.
322 Rosen, R. 1987. “On Complex Systems.”, European Journal of Operational Research 30, 129-134.
323 G. C. Rota : On the foundation of combinatorial theory, I. The theory of M'́obius functions, Zetschrif f'́ur Wahrscheinlichkeitstheorie 2 (1968), 340.
324 Rovelli, C.: 1998, Loop Quantum Gravity, in N. Dadhich, et al. Living Reviews in Relativity (refereed electronic journal) online download
325 Schrödinger E.: 1967, Mind and Matter in ‘What is Life?’, Cambridge University Press: Cambridge, UK.
326 Schrödinger E.: 1945, What is Life?, Cambridge University Press: Cambridge, UK.
327 Scott, P. J., 2000, Some Aspects of Categories in Computer Science, Handbook of Algebra, Vol. 2, Amsterdam: North Holland, 3–77.
328 Seely, R. A. G., 1984, “Locally Cartesian Closed Categories and Type Theory”, Mathematical Proceedings of the Cambridge Mathematical Society, 95, no. 1, 33–48.
329 Shapiro, S., 2005, “Categories, Structures and the Frege-Hilbert Controversy: the Status of Metamathematics”, Philosophia Mathematica, 13, 1, 61–77.
330 Sorkin, R.D. 1991. “Finitary substitute for continuous topology.”, Int. J. Theor. Phys. 30 No. 7.: 923–947.
331 Smolin, L.: 2001, Three Roads to Quantum Gravity, Basic Books: New York.
332 Spanier, E. H.: 1966, Algebraic Topology, McGraw Hill: New York.
333 Spencer–Brown, G.: 1969, Laws of Form, George Allen and Unwin, London.
334 Stapp, H.: 1993, Mind, Matter and Quantum Mechanics, Springer Verlag: Berlin–Heidelberg–New York.
335 Stewart, I. and Golubitsky, M. : 1993. “Fearful Symmetry: Is God a Geometer?”, Blackwell: Oxford, UK.
336 Szabo, R. J.: 2003, Quantum field theory on non-commutative spaces, Phys. Rep. 378: 207–209.
337 Tattersall, I. and J. Schwartz: 2000, Extinct Humans. Westview Press, Boulder, Colorado and Cumnor Hill Oxford. ISBN 0-8133-3482-9 (hc)
338 Thom, R.: 1980, Modèles mathématiques de la morphogénèse, Paris, Bourgeois.
339 Thompson, W. D’ Arcy. 1994. On Growth and Form., Dover Publications, Inc: New York.
340 uring, A.M. 1952. The Chemical Basis of Morphogenesis, Philosophical Trans. of the the Royal Soc.(B) 257:37-72.
341 Taylor, P., 1996, “Intuitionistic sets and Ordinals.”, Journal of Symbolic Logic, 61, 705–744.
342 Taylor, P., 1999, “Practical Foundations of Mathematics.”, Cambridge: Cambridge University Press.
343 Tierney, M., 1972, “Sheaf Theory and the Continuum Hypothesis”, in Toposes, Algebraic Geometry and Logic,
344 Unruh, W.G.: 2001, “Black holes, dumb holes, and entropy”, in C. Callender and N. Hugget (eds. ) Physics Meets Philosophy at the Planck scale, Cambridge University Press, pp. 152–173.
345 Van der Hoeven, G. & Moerdijk, I., 1984a, “Sheaf Models for Choice Sequences”, Annals of Pure and Applied Logic, 27, no. 1, 63–107.
346 Van der Hoeven, G. & Moerdijk, I., 1984b, “On Choice Sequences determined by Spreads”, Journal of Symbolic Logic, 49, no. 3, 908–916.
347 Várilly, J. C.: 1997, An introduction to noncommutative geometry ( $arXiv:physics/9709045$ ).
348 von Neumann, J.: 1932, Mathematische Grundlagen der Quantenmechanik, Springer: Berlin.
349 Wallace, R. 2005. Consciousness : A Mathematical Treatment of the Global Neuronal Workspace, Springer: Berlin.
350 Weinstein, A. 1996. “Groupoids : unifying internal and external symmetry.”, Notices of the Amer. Math. Soc. 43: 744–752.
351 Wess J. and J. Bagger. 1983. Supersymmetry and Supergravity, Princeton University Press: Princeton, NJ.
352 Weinberg, S. 1995. The Quantum Theory of Fields vols. 1 to 3, Cambridge Univ. Press.
353 Wheeler, J. and W. Zurek. 1983. Quantum Theory and Measurement, Princeton University Press: Princeton, NJ.
354 Whitehead, J. H. C. 1941. “On adding relations to homotopy groups.”, Annals of Math. 42 (2): 409-428.
355 Wiener, N.: 1950, The Human Use of Human Beings: Cybernetics and Society. Free Association Books: London, 1989 edn.
356 Woit, P.: 2006, Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Laws, Jonathan Cape.
357 Wood, R.J., 2004, Ordered Sets via Adjunctions, Categorical Foundations, M. C. Pedicchio & W. Tholen, eds., Cambridge: Cambridge University Press.

Keywords:

references on category theory, toposes, categories of logic algebras, computers, automata theory in biology and medicine, biomathematics and physics applications

Synonym:

references on algebraic topology, category theory, categories of logic algebras, biomathematics and physics applications

Type of Math Object:

Bibliography

Major Section:

Reference

Parent:

overview of the content of PlanetMath

Groups audience:

Editing Group for CategoricalOntologyABibliographyOfCategoryTheory

Mathematics Subject Classification

92B99 None of the above, but in MSC2010 section 92Bxx
92B10 Taxonomy, cladistics, statistics
92B05 General biology and biomathematics
55U30 Duality
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18C99 None of the above, but in MSC2010 section 18Cxx
18A25 Functor categories, comma categories
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
18A05 Definitions, generalizations
18C99 None of the above, but in MSC2010 section 18Cxx
18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
03-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
00A15 Bibliographies

Add a correction
Attach a problem
Ask a question

User menu

bibliography in algebraic topology,categories and QAT

Primary tabs

bibliography in algebraic topology,categories and QAT

0.1 Literature for the following areas of mathematics:

References

Mathematics Subject Classification

Recent Activity

Info

Versions

User menu

User login

You are here

bibliography in algebraic topology,categories and QAT

Primary tabs

bibliography in algebraic topology,categories and QAT

0.1 Literature for the following areas of mathematics:

References

Mathematics Subject Classification

Search form

Recent Activity

Info

Versions