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PlanetPhysics/Bibliography for Quantum Algebraic Topology and Categories

< PlanetPhysics

\subsubsection{A list of references in: Algebraic topology, quantum algebraic topology, n-logic algebraic categories, Theory of Categories, functors, natural transformations, Topoi and categorical ontology.}

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

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References

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  2. ↑ Alfsen, E.M. and F. W. Schultz: \emph{Geometry of State Spaces of Operator Algebras}, Birkh\"auser, 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.
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  10. ↑ Baez, J. and Dolan, J., 1998b, "Categorification", Higher Category Theory, Contemporary Mathematics, 230, Providence: AMS, 1-36.
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  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.
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  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.
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  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.
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  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).
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  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.
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