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Bibliography: References

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Topical references for Categories and Algebraic Topology Applications in Theoretical Physics

1. 1,Adámek, J.. et al., Locally Presentable and Accessible Categories, Cambridge: Cambridge University Press (1994).
2. 2 Alfsen, E.M. and F. W. Schultz: Geometry of State Spaces of Operator Algebras, Birkh'auser, Boston-Basel-Berlin (2003).
3. 3 Atiyah, M.F. 1956. On the Krull-Schmidt theorem with applications to sheaves. Bull. Soc. Math. France, 84: 307-317.
4. 3. 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. 5 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. 6 Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective, Philosophia Mathematica, 3, 209-237.
9. 7 Awodey, S., 2004, An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism., Philosophia Mathematica, 12, 54-64.
10. 8 Awodey, S., 2006, Category Theory, Oxford: Clarendon Press.
11. 9 Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes., Advances in Mathematics, 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.

1. 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 Baianu, I.C.: 1971a, Organismic Supercategories and Qualitative Dynamics of Systems. Ibid., 33 (3), 339-354. 15 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. 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 Łukasiewicz Algebras: The Non-linear Theory. Bulletin of Mathematical Biology, 39: 249-258. 20 Baianu, I.C.: 1980a, Natural Transformations of Organismic Structures., Bulletin of Mathematical Biology,42: 431-446. 20 Baianu, I. C.: 1983, Natural Transformation Models in Molecular Biology., in Proceedings of the SIAM Natl. Meet., Denver,CO.; Eprint at cogprints.org/3675 20 Baianu, I.C.: 1984, A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Networks, FASEB Proceedings 43, 917. 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. Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models (2004). Eprint: w. Cogprints at Sussex Univ. 24 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). 25 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. 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).

1. 31 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.
2. 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.
3. 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.
4. 34 Baianu, I.C. et al. Quantum Algebra and Symmetries. PediaPress:Mainz, Germany, 1,112 pages, volumes I-III, Second edition. Books: ``Quantum Algebra and Symmetries
5. 35 M. Barr and C. Wells. Toposes, Triples and Theories. Montreal: McGill University, 2000.
6. 36 Barr, M. & Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.
7. 37 Barr, M. & Wells, C., 1999, Category Theory for Computing Science, Montreal: CRM.
8. 38 Batanin, M., 1998, Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories", Advances in Mathematics, 136, 39-103.
9. 39 Bell, J. L., 1981, Category Theory and the Foundations of Mathematics, British Journal for the Philosophy of Science, 32, 349-358.
10. 40 Bell, J. L., 1982, Categories, Toposes and Sets, Synthese,51, 3, 293-337.

41 Bell, J. L., 1986, From Absolute to Local Mathematics, Synthese, 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, 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 , 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: Algèbre commutative., in Éléments de Mathématique., 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, Applied Categorical Structures 12: 63-80. 54 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 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 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. 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