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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.: 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.
  22. ↑ Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures, in Proceed. Relational Biology Symp. Argentina; CERN Preprint No.EXT-2004-067 .
  23. ↑ 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.
  24. ↑ 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).
  25. ↑ 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.
  26. ↑ Baianu, I.C.: 2004a, Quantum Nano--Automata (QNA): Microphysical Measurements with Microphysical QNA Instruments, CERN Preprint EXT--2004--125 .
  27. ↑ Baianu, I. C.: 2004b, Quantum Interactomics and Cancer Mechanisms, Preprint 00001978 .
  28. ↑ Baianu, I. C.: 2006, Robert Rosen's Work and Complex Systems Biology, Axiomathes 16 (1--2):25--34.
  29. ↑ Baianu, I. C., Brown, R. and J. F. Glazebrook: 2006, Quantum Algebraic Topology and Field Theories. Preprint
  30. ↑ Baianu, I.C.: 2008, Translational Genomics and Human Cancer Interactomics, (invited Review, submitted in November 2007 to Translational Oncogenomics ).
  31. ↑ 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.
  32. ↑ 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.
  33. ↑ Baianu, I.C., R. Brown and J. F. Glazebrook: 2007b, A Non-Abelian, Categorical Ontology of Spacetimes and Quantum Gravity, Axiomathes, 17: 169-225.
  34. ↑ M.~Barr and C.~Wells. Toposes, Triples and Theories . Montreal: McGill University, 2000.
  35. ↑ Barr, M. \& Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.
  36. ↑ Barr, M. \& Wells, C., 1999, Category Theory for Computing Science, Montreal: CRM.
  37. ↑ Batanin, M., 1998, Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories", Advances in Mathematics, 136, 39--103.
  38. ↑ Bell, J. L., 1981, Category Theory and the Foundations of Mathematics, British Journal for the Philosophy of Science, 32, 349--358.
  39. ↑ Bell, J. L., 1982, Categories, Toposes and Sets, Synthese ,{\mathbf 51}, 3, 293--337.
  40. ↑ Bell, J. L., 1986, From Absolute to Local Mathematics, Synthese , {\mathbf 69}, 3, 409--426.
  41. ↑ Bell, J. L., 1988, Toposes and Local Set Theories: An Introduction , Oxford: Oxford University Press.
  42. ↑ Birkoff, G. and Mac Lane, S., 1999, Algebra, 3rd ed., Providence: AMS.
  43. ↑ Biss, D.K., 2003, Which Functor is the Projective Line?, American Mathematical Monthly , {\mathbf 110}, 7, 574--592.
  44. ↑ Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111--140.
  45. ↑ Blass, A. and Scedrov, A., 1989, Freyd's Model for the Independence of the Axiom of Choice, Providence: AMS.
  46. ↑ 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.
  47. ↑ Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5-29.
  48. ↑ Blute, R. \& Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science
  49. ↑ Borceux, F.: 1994, Handbook of Categorical Algebra , vols: 1--3, in Encyclopedia of Mathematics and its Applications 50 to 52 , Cambridge University Press.
  50. ↑ Bourbaki, N. 1961 and 1964: Alg\`{e bre commutative.}, in \'{E}l\'{e}ments de Math\'{e}matique., Chs. 1--6., Hermann: Paris.
  51. ↑ R. Brown: Topology and Groupoids , BookSurge LLC (2006).
  52. ↑ 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.
  53. ↑ 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
  54. ↑ 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.
  55. ↑ 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.
  56. ↑ 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.
  57. ↑ 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.
  58. ↑ Brown, R., and Hardy, J.P.L.:1976, Topological groupoids I: universal constructions, Math. Nachr. , 71: 273-286.
  59. ↑ 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.
  60. ↑ Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, Cah. Top. G\'{e om. Diff.} 17 , 343-362.
  61. ↑ 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.
  62. ↑ 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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  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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