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 theoryMathworldPlanetmathPlanetmathPlanetmathPlanetmath can be found on the web at: http://plato.stanford.edu/entries/category-theory/Plato, Stanford Encyclopedia of Philosophy web site.

0.1 Literature for the following areas of mathematics:

References

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  • 2 Alfsen, E.M. and F. W. Schultz: Geometry of State SpacesMathworldPlanetmath 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. AlgebraMathworldPlanetmath, 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 MetalogicMathworldPlanetmath., 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, StructureMathworldPlanetmath 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 SetsMathworldPlanetmath 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 SupercategoriesPlanetmathPlanetmathPlanetmathPlanetmath: Towards a UnitaryPlanetmathPlanetmath 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 AlgebraicMathworldPlanetmathPlanetmath 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.; http://cogprints.org/3675/1/Naturaltransfmolbionu6.pdfEprint 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: http://doe.cern.ch//archive/electronic/other/ext/ext-2004-072.pdfCERN Preprint No. EXT-2004-072 , and http://en.scientificcommons.org/1857371html Abstract.
  • 27 Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures, in Proceed. Relational Biology Symp. Argentina; http://doc.cern.ch//archive/electronic/other/ext/ext-2004-067.pdfCERN 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). http://doc.cern.ch//archive/electronic/other/ext/ext-2004-059.pdfCERN 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 RelationMathworldPlanetmathPlanetmathPlanetmath to Dynamic Bionetworks, (M,R)–Systems and Their Higher Dimensional Algebra, http://fs512.fshn.uiuc.edu/QAuto.pdfAbstract 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, http://doc.cern.ch//archive/electronic/other/ext/ext-2004-118.pdfPreprint 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. http://fs512.fshn.uiuc.edu/QAT.pdfPreprint
  • 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: TransformationsPlanetmathPlanetmath 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-AbelianMathworldPlanetmathPlanetmath, Categorical Ontology of Spacetimes and Quantum Gravity, Axiomathes, 17: 169-225.
  • 39 Baianu, I.C. et al. Quantum Algebra and SymmetriesPlanetmathPlanetmath. PediaPress:Mainz, Germany, 1,112 pages, volumes I-III, Second edition. http://planetmath.org/?op=getobj&from=books&id=281PM 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 TheoriesMathworldPlanetmath: 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 ForcingMathworldPlanetmath , 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 ChoiceMathworldPlanetmath, Providence: AMS.
  • 52 Blass, A. and Scedrov, A., 1992, CompletePlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath 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 commutativePlanetmathPlanetmathPlanetmathPlanetmath., 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 groupoidPlanetmathPlanetmath 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.
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  • 60 Brown, R., Glazebrook, J. F. and I.C. Baianu.: 2007b, A Conceptual, Categorical and Higher Dimensional Algebra Framework of UniversalPlanetmathPlanetmathPlanetmath 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 languagePlanetmathPlanetmath 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 groupoidsPlanetmathPlanetmathPlanetmathPlanetmath 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 groupoidsPlanetmathPlanetmathPlanetmath 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 presentationsMathworldPlanetmathPlanetmath of modules of identitiesPlanetmathPlanetmathPlanetmathPlanetmath 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 homologyMathworldPlanetmathPlanetmath 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 HypothesisMathworldPlanetmath”, 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.
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  • 82 Cohen, P.M. 1965. Universal AlgebraMathworldPlanetmath, 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 colimitsMathworldPlanetmath.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 geometryPlanetmathPlanetmath. 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 AlgebrasMathworldPlanetmathPlanetmathPlanetmath, 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 bundlesMathworldPlanetmath 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.
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  • 112 Eilenberg, S.: 1960. Abstract description of some basic functors., J. Indian Math.Soc., 24 :221-234.
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  • 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 algebra and Grassmannian solitons in multicomponent Hall systems, arXiv:hep–th/0209198.
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  • 117 Fell, J. M. G., 1960. “The Dual SpacesMathworldPlanetmathPlanetmath of C*–Algebras”, Transactions of the American Mathematical Society, 94: 365–403.
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  • 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 CategoriesMathworldPlanetmathPlanetmathPlanetmath. 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 productPlanetmathPlanetmath 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 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.]
  • 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, “PresheafMathworldPlanetmathPlanetmathPlanetmath 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, LocalizationMathworldPlanetmath in non-commutative noetherian ringsMathworldPlanetmath, 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.,TopologyMathworldPlanetmath, 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 ExtensionPlanetmathPlanetmathPlanetmath of the Dijkgraaf-Witten Invariant to Categorical math.QA/0608484[abs,ps,pdf,other].
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  • 152 K.A. Hardie, K.H. Kamps and R.W. Kieboom, A homotopyMathworldPlanetmathPlanetmath 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 groupoidsPlanetmathPlanetmath, 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 ω-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.
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Title bibliography in algebraic topology,categories and QAT
Canonical name BibliographyInAlgebraicTopologycategoriesAndQAT
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Numerical id 178
Author bci1 (20947)
Entry type Bibliography
Classification msc 92B99
Classification msc 92B10
Classification msc 92B05
Classification msc 55U30
Classification msc 18A40
Classification msc 18C99
Classification msc 18A25
Classification msc 18A30
Classification msc 18A05
Classification msc 18C99
Classification msc 18-00
Classification msc 03-00
Classification msc 00A15
Synonym references on algebraic topology
Synonym category theory
Synonym categories of logic algebras
Synonym biomathematics and physics applications
Related topic BibliographyForTopology
Related topic IndexOfCategoryTheory
Related topic HomotopyGroupoidsAndCrossComplexesAsNonCommutativeStructuresInHigherDimensionalAlgebraHDA
Related topic CategoryTheory
Related topic AlgebraicTopology
Related topic SupercategoriesOfComplexSystems
Related topic ETAS
Related topic IndexOfCategories