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PlanetPhysics/Categories and QAT Bibliography Algebraic Topology

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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 the Plato, Stanford Encyclopedia of Philosophy web site on category theory and its applications.

Literature for the following areas of mathematics:

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References

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  1. ↑ Ad\'amek, J.. et al., Locally Presentable and Accessible Categories, Cambridge: Cambridge University Press (1994).
  2. ↑ Alfsen, E.M. and F. W. Schultz: \emph{Geometry of State Spaces of Operator Algebras}, Birkhauser, Boston--Basel--Berlin (2003).
  3. ↑ 3.0 3.1 Atiyah, M.F. 1956. On the Krull-Schmidt theorem with applications to sheaves. Bull. Soc. Math. France , 84 : 307--317. Cite error: Invalid <ref> tag; name "AMF56" defined multiple times with different content
  4. ↑ Awodey, S. \& Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168--1182.
  5. ↑ 5.0 5.1 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. Cite error: Invalid <ref> tag; name "AS-RER2k2" defined multiple times with different content
  6. ↑ Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective, Philosophia Mathematica , {\mathbf 3}, 209-237.
  7. ↑ Awodey, S., 2004, An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism., Philosophia Mathematica , {\mathbf 12}, 54-64.
  8. ↑ Awodey, S., 2006, Category Theory , Oxford: Clarendon Press.
  9. ↑ Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes., Advances in Mathematics , {\mathbf 135}, 145--206.
  10. ↑ Baez, J. and Dolan, J., 1998b, "Categorification", Higher Category Theory, Contemporary Mathematics, 230, Providence: AMS, 1-36.
  11. ↑ Baez, J. and Dolan, J., 2001, "From Finite Sets to Feynman Diagrams", Mathematics Unlimited -- 2001 and Beyond , Berlin: Springer, 29-50.
  12. ↑ Baez, J., 1997, "An Introduction to n-Categories", Category Theory and Computer Science , Lecture Notes in Computer Science, 1290, Berlin: Springer-Verlag, 1--33.
  13. ↑ Baianu, I.C. and M. Marinescu: 1968, Organismic Supercategories: Towards a Unitary Theory of Systems. Bulletin of Mathematical Biophysics 30 , 148-159.
  14. ↑ Baianu, I.C.: 1970, Organismic Supercategories: II. On Multistable Systems. Bulletin of Mathematical Biophysics , 32 : 539-561.
  15. ↑ 15.0 15.1 Baianu, I.C.: 1971a, Organismic Supercategories and Qualitative Dynamics of Systems. Ibid. , 33 (3), 339--354. Cite error: Invalid <ref> tag; name "ICB4" defined multiple times with different content
  16. ↑ Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems. Bulletin of Mathematical Biophysics , 35 (4), 475--486.
  17. ↑ Baianu, I.C.: 1973, Some Algebraic Properties of (M,R) -- Systems. Bulletin of Mathematical Biophysics 35 , 213-217.
  18. ↑ 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.
  19. ↑ Baianu, I.C.: 1977, A Logical Model of Genetic Activities in \L{}ukasiewicz Algebras: The Non-linear Theory. Bulletin of Mathematical Biology , 39 : 249-258.
  20. ↑ 20.0 20.1 20.2 Baianu, I.C.: 1980a, Natural Transformations of Organismic Structures., Bulletin of Mathematical Biology ,42 : 431-446. Cite error: Invalid <ref> tag; name "ICB2" defined multiple times with different content
  21. ↑ Baianu, I.C., H. S. Gutowsky, and E. Oldfield: 1984, Proc. Natl. Acad. Sci. USA , 81 (12): 3713-3717.
  22. ↑ 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.
  23. ↑ Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures, in Proceed. Relational Biology Symp. Argentina; CERN Preprint No.EXT-2004-067 .
  24. ↑ Baianu, I.C.: 2004a. \L{}ukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models (2004). Eprint: w. Cogprints at Sussex Univ.
  25. ↑ Baianu, I.C.: 2004b \L{}ukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamics). CERN EXT-2004-059,Health Physics and Radiation Effects , (June 29, 2004).
  26. ↑ Baianu, I. C., Glazebrook, J. F. and G. Georgescu: 2004, Categories of Quantum Automata and N-Valued \L ukasiewicz Algebras in Relation to Dynamic Bionetworks, (M,R) --Systems and Their Higher Dimensional Algebra, Abstract and Preprint of Report.
  27. ↑ Baianu, I.C.: 2004a, Quantum Nano--Automata (QNA): Microphysical Measurements with Microphysical QNA Instruments, CERN Preprint EXT--2004--125 .
  28. ↑ Baianu, I. C.: 2004b, Quantum Interactomics and Cancer Mechanisms, Preprint 00001978 .
  29. ↑ Baianu, I. C.: 2006, Robert Rosen's Work and Complex Systems Biology, Axiomathes 16 (1--2):25--34.
  30. ↑ Baianu, I. C., Brown, R. and J. F. Glazebrook: 2006, Quantum Algebraic Topology and Field Theories. Preprint
  31. ↑ Baianu, I.C.: 2008, Translational Genomics and Human Cancer Interactomics, (invited Review, submitted in November 2007 to Translational Oncogenomics ).
  32. ↑ Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006b, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and \L ukasiewicz--Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., Axiomathes , 16 Nos. 1--2: 65--122.
  33. ↑ 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.
  34. ↑ Baianu, I.C., R. Brown and J. F. Glazebrook: 2007b, A Non-Abelian, Categorical Ontology of Spacetimes and Quantum Gravity, Axiomathes, 17: 169-225.
  35. ↑ M.~Barr and C.~Wells. Toposes, Triples and Theories . Montreal: McGill University, 2000.
  36. ↑ Barr, M. \& Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.
  37. ↑ Barr, M. \& Wells, C., 1999, Category Theory for Computing Science, Montreal: CRM.
  38. ↑ Batanin, M., 1998, Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories", Advances in Mathematics, 136, 39--103.
  39. ↑ Bell, J. L., 1981, Category Theory and the Foundations of Mathematics, British Journal for the Philosophy of Science, 32, 349--358.
  40. ↑ Bell, J. L., 1982, Categories, Toposes and Sets, Synthese ,{\mathbf 51}, 3, 293--337.
  41. ↑ Bell, J. L., 1986, From Absolute to Local Mathematics, Synthese , {\mathbf 69}, 3, 409--426.
  42. ↑ Bell, J. L., 1988, Toposes and Local Set Theories: An Introduction , Oxford: Oxford University Press.
  43. ↑ Birkoff, G. and Mac Lane, S., 1999, Algebra, 3rd ed., Providence: AMS.
  44. ↑ Biss, D.K., 2003, Which Functor is the Projective Line?, American Mathematical Monthly , {\mathbf 110}, 7, 574--592.
  45. ↑ Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111--140.
  46. ↑ Blass, A. and Scedrov, A., 1989, Freyd's Model for the Independence of the Axiom of Choice, Providence: AMS.
  47. ↑ Blass, A. and Scedrov, A., 1992, Complete Topoi Representing Models of Set Theory, Annals of Pure and Applied Logic , {\mathbf 57}, no. 1, 1-26.
  48. ↑ Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5-29.
  49. ↑ Blute, R. \& Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science
  50. ↑ Borceux, F.: 1994, Handbook of Categorical Algebra , vols: 1--3, in Encyclopedia of Mathematics and its Applications 50 to 52 , Cambridge University Press.
  51. ↑ Bourbaki, N. 1961 and 1964: Alg\`{e bre commutative.}, in \'{E}l\'{e}ments de Math\'{e}matique., Chs. 1--6., Hermann: Paris.
  52. ↑ R. Brown: Topology and Groupoids , BookSurge LLC (2006).
  53. ↑ Brown, R. and G. Janelidze: 2004, Galois theory and a new homotopy double groupoid of a map of spaces, \emph{Applied Categorical Structures} 12 : 63-80.
  54. ↑ Brown, R., Higgins, P. J. and R. Sivera,: 2007a, \emph{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
  55. ↑ 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.
  56. ↑ Brown, R., Paton, R. and T. Porter.: 2004, Categorical language and hierarchical models for cell systems, in \emph{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.
  57. ↑ 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.
  58. ↑ Brown, R., Hardie, K., Kamps, H. and T. Porter: 2002, The homotopy double groupoid of a Hausdorff space., \emph{Theory and Applications of Categories} 10 , 71-93.
  59. ↑ Brown, R., and Hardy, J.P.L.:1976, Topological groupoids I: universal constructions, Math. Nachr. , 71: 273-286.
  60. ↑ Brown, R. and T. Porter: 2006, Category Theory: an abstract setting for analogy and comparison, In: What is Category Theory?, \emph{Advanced Studies in Mathematics and Logic, Polimetrica Publisher}, Italy, (2006) 257-274.
  61. ↑ Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, Cah. Top. G\'{e om. Diff.} 17 , 343-362.
  62. ↑ 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.
  63. ↑ 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.
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  137. ↑ Grothendieck, A.: 1957, Sur quelque point d-alg\'{e}bre homologique. , Tohoku Math. J. , 9: 119-121.
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  141. ↑ Groups Authors: J. Faria Martins, Timothy Porter., On Yetter's Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical  .
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  333. ↑ Wallace, R. 2005. Consciousness : A Mathematical Treatment of the Global Neuronal Workspace , Springer: Berlin.
  334. ↑ Weinstein, A. 1996. "Groupoids : unifying internal and external symmetry.", Notices of the Amer. Math. Soc. 43 : 744--752.
  335. ↑ Wess J. and J. Bagger. 1983. Supersymmetry and Supergravity , Princeton University Press: Princeton, NJ.
  336. ↑ Weinberg, S. 1995. The Quantum Theory of Fields vols. 1 to 3, Cambridge Univ. Press.
  337. ↑ Wheeler, J. and W. Zurek. 1983. Quantum Theory and Measurement , Princeton University Press: Princeton, NJ.
  338. ↑ Whitehead, J. H. C. 1941. "On adding relations to homotopy groups.", Annals of Math. 42 (2): 409-428.
  339. ↑ Wiener, N.: 1950, \emph{The Human Use of Human Beings: Cybernetics and Society.} Free Association Books: London, 1989 edn.
  340. ↑ Woit, P.: 2006, Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Laws , Jonathan Cape.
  341. ↑ Wood, R.J., 2004, Ordered Sets via Adjunctions, Categorical Foundations , M. C. Pedicchio \& W. Tholen, eds., Cambridge: Cambridge University Press.

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