Talk:PlanetPhysics/Bibliography for Mathematical Physics Foundations

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\begin{document}

 \section{Bibliography for mathematical physics foundations}

A1. \textbf{Axiomatics and \htmladdnormallink{categories}{http://planetphysics.us/encyclopedia/Cod.html} in the foundations of physics}

\begin{thebibliography}{99}

\bibitem{AS}
Alfsen, E.M. and F. W. Schultz: \emph{Geometry of State Spaces of
Operator Algebras}, Birkh\"auser, Boston--Basel--Berlin (2003).

\bibitem{AMF56}
Atiyah, M.F. 1956. On the Krull-Schmidt theorem with applications to sheaves.
\emph{Bull. Soc. Math. France}, \textbf{84}: 307--317.

\bibitem{AMF56}
Auslander, M. 1965. Coherent Functors. \emph{Proc. Conf. Cat. Algebra, La Jolla},
189--231.

\bibitem{AS-BC2k}
Awodey, S. \& Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168--1182.

\bibitem{AS-RER2k2}
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.

\bibitem{AS-RER2k2}
Awodey, S. \& Reck, E. R., 2002, Completeness and Categoricity II. Twentieth-Century Metalogic to Twenty-first-Century Semantics, \emph{History and Philosophy of Logic}, 23, (2): 77--94.

\bibitem{AS96}
Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective,
\emph{Philosophia Mathematica}, 3: 209--237.

\bibitem{AS2k4}
Awodey, S., 2004, An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism, \emph{Philosophia Mathematica}, 12: 54--64.

\bibitem{AS2k6}
Awodey, S., 2006, Category Theory, Oxford: Clarendon Press.

\bibitem{BAJ-DJ98a}
Baez, J. \& Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes,
in: \emph{Advances in Mathematics}, 135, 145--206.

\bibitem{BAJ-DJ98B}
Baez, J. \& Dolan, J., 1998b, ``Categorification", Higher Category Theory, Contemporary Mathematics, 230, Providence: AMS, 1--36.

\bibitem{BAJ-DJ2k1}
Baez, J. \& Dolan, J., 2001, From Finite Sets to Feynman Diagrams,
in \emph{Mathematics Unlimited -- 2001 and Beyond}, Berlin: Springer, 29--50.

\bibitem{BAJ-DJ97}
Baez, J., 1997, An Introduction to n-Categories,
in \emph{Category Theory and Computer Science, Lecture Notes in Computer Science}, 1290, Berlin: Springer-Verlag, 1--33.

\bibitem{ICB4}
Baianu, I.C.: 1971a, Organismic Supercategories and Qualitative Dynamics of Systems. \emph{Ibid.}, \textbf{33} (3), 339--354.

\bibitem{ICB4}
Baianu, I.C.: 1971b, Categories, Functors and Quantum Algebraic
Computations, in P. Suppes (ed.), \emph{Proceed. Fourth Intl. Congress Logic-Mathematics-Philosophy of Science}, September 1--4, 1971, Bucharest.

\bibitem{ICB-HG-EO84}
Baianu, I.C., H. S. Gutowsky, and E. Oldfield: 1984, {\em Proc. Natl. Acad. Sci. USA}, \textbf{81}(12):
3713-3717.

\bibitem{Bgg2}
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, \textbf{(M,R)}--Systems and Their Higher Dimensional Algebra,
\htmladdnormallink{PDF's of Abstract and Preprint of Report}{\\http://www.ag.uiuc.edu/fs401/QAuto.pdf}.

\bibitem{ICB8}
Baianu, I.C.: 2004a, Quantum Nano--Automata (QNA): Microphysical Measurements with Microphysical QNA Instruments, \emph{CERN Preprint EXT--2004--125}.

\bibitem{Bgb2}
Baianu, I. C., Brown, R. and J. F. Glazebrook: 2006a, {\em Quantum Algebraic Topology and Field Theories}.
\htmladdnormallink{Preprint subm.}{http://www.ag.uiuc.edu/fs40l/QAT.pdf}.

\bibitem{BBGG1}
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., \emph{Axiomathes}, \textbf{16} Nos. 1--2: 65--122.

\bibitem{Bggb4}
Baianu, I.C., R. Brown and J. F. Glazebrook: 2007b, A Non-Abelian, Categorical Ontology of Spacetimes and Quantum Gravity, Axiomathes, 17: 169-225.

\bibitem{Ba-We2k}
M.~Barr and C.~Wells. {\em Toposes, Triples and Theories}. Montreal: McGill University, 2000.

\bibitem{Ba-We85}
Barr, M. \& Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.

\bibitem{BM-CW99}
Barr, M. \& Wells, C., 1999, Category Theory for Computing Science, Montreal: CRM.

\bibitem{BaM98}
Batanin, M., 1998, Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories,
\emph{Advances in Mathematics}, 136: 39--103.

\bibitem{BJL81}
Bell, J. L., 1981, Category Theory and the Foundations of Mathematics,
\emph{British Journal for the Philosophy of Science}, 32, 349--358.

\bibitem{BJL82}
Bell, J. L., 1982, Categories, Toposes and Sets, \emph{Synthese}, 51, 3, 293--337.

\bibitem{BJL86}
Bell, J. L., 1986, From Absolute to Local Mathematics, \emph{Synthese}, 69, 3, 409--426.

\bibitem{BJL88}
Bell, J. L., 1988, Toposes and Local Set Theories: An Introduction, Oxford: Oxford University Press.

\bibitem{BG-MCLS99}
Birkoff, G. \& Mac Lane, S., 1999, Algebra, 3rd ed., Providence: AMS.

\bibitem{BDK2k3}
Biss, D.K., 2003, Which Functor is the Projective Line?, \emph{American Mathematical Monthly}, 110, 7, 574--592.

\bibitem{BA-SA83}
Blass, A. \& Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111--140.

\bibitem{BA-SA89}
Blass, A. \& Scedrov, A., 1989, Freyd's Model for the Independence of the Axiom of Choice, Providence: AMS.

\bibitem{BASA92}
Blass, A. \& Scedrov, A., 1992, Complete Topoi Representing Models of Set Theory,
\emph{Annals of Pure and Applied Logic}, 57, no. 1, 1--26.

\bibitem{BA84}
Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5--29.

\bibitem{BR-SP2k4}
Blute, R. \& Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science

\bibitem{Borceux94}
Borceux, F.: 1994, \emph{Handbook of Categorical Algebra}, vols: 1--3,
in {\em Encyclopedia of Mathematics and its Applications} \textbf{50} to \textbf{52}, Cambridge University Press.

\bibitem{Bourbaki1}
Bourbaki, N. 1961 and 1964: \emph{Alg\`{e}bre commutative.},
in \'{E}l\'{e}ments de Math\'{e}matique., Chs. 1--6., Hermann: Paris.

\bibitem{BrownBook1}
R. Brown: \emph{Topology and Groupoids}, BookSurge LLC (2006).

\bibitem{BJk4}
Brown, R. and G. Janelidze: 2004, Galois theory and a new homotopy
double groupoid of a map of spaces, \emph{Applied Categorical
Structures} \textbf{12}: 63-80.

\bibitem{BHR2}
Brown, R., Higgins, P. J. and R. Sivera,: 2007a, \emph{Non-Abelian
Algebraic Topology},\htmladdnormallink{Vol.I PDF}{http://www.bangor.ac.uk/~mas010/nonab-t/partI010604.pdf}.

\bibitem{BGB2k7b}
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., \emph{Axiomathes} (17): 321--379.

\bibitem{BPP2k4}
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.

\bibitem{BP2k3}
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.

\bibitem{Br-Har-Ka-Po2k2}
Brown, R., Hardie, K., Kamps, H. and T. Porter: 2002, The homotopy
double groupoid of a Hausdorff space., \emph{Theory and
Applications of Categories} \textbf{10}, 71-93.

\bibitem{Br-Hardy76}
Brown, R., and Hardy, J.P.L.:1976, Topological groupoids I:
universal constructions, \emph{Math. Nachr.}, 71: 273-286.

\bibitem{Br-Po-analogy2k6}
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.

\bibitem{Br-Sp76}
Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed
modules, \emph{Cah. Top. G\'{e}om. Diff.} \textbf{17}, 343-362.

\bibitem{BRTPT2k6}
Brown R, and Porter T (2006) Category theory: an abstract setting for analogy and comparison. In: What is
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257-274.

\bibitem{BR-SCB76}
Brown R, Razak Salleh A (1999) Free crossed resolutions of groups and presentations of modules of
identities among relations. {\em LMS J. Comput. Math.}, \textbf{2}: 25--61.

\bibitem{BDA55}
Buchsbaum, D. A.: 1955, Exact categories and duality., Trans. Amer. Math. Soc. \textbf{80}: 1-34.

\bibitem{BDA55}
Buchsbaum, D. A.: 1969, A note on homology in categories., Ann. of Math. \textbf{69}: 66-74.

\bibitem{BI65}
Bucur, I. (1965). {\em Homological Algebra}. (orig. title: ``Algebra Omologica'')
Ed. Didactica si Pedagogica: Bucharest.

\bibitem{BI-DA68}
Bucur, I., and Deleanu A. (1968). {\em Introduction to the Theory of Categories and Functors}. J.Wiley and Sons: London

\bibitem{BL2k3}
Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes, \emph{Adv. in Math.} \textbf{179}, 291-317.

\bibitem{BM74}
Bunge, M., 1974, "Topos Theory and Souslin's Hypothesis", Journal of Pure and Applied Algebra, 4, 159-187.

\bibitem{BM84}
Bunge, M., 1984, "Toposes in Logic and Logic in Toposes", Topoi, 3, no. 1, 13-22.

\bibitem{BM-LS2k3}
Bunge M, Lack S (2003) Van Kampen theorems for toposes. {\em Adv Math}, \textbf {179}: 291-317.

\bibitem{BJ-ICJ2k1}
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.

\bibitem{BJ-ICJ98-2k2}
Butterfield J., Isham C.J. 1998, 1999, 2000-2002, A topos perspective on the Kochen-Specker theorem
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\bibitem{CH-ES56}
Cartan, H. and Eilenberg, S. 1956. {\em Homological Algebra}, Princeton Univ. Press: Pinceton.

\bibitem{Chaician}
M. Chaician and A. Demichev. 1996. Introduction to Quantum Groups, World Scientific .

\bibitem{CC46}
Chevalley, C. 1946. The theory of Lie groups. Princeton University Press, Princeton NJ

\bibitem{CPM65}
Cohen, P.M. 1965. {\em Universal Algebra}, Harper and Row: New York, london and Tokyo.

\bibitem{CF}
M. Crainic and R. Fernandes.2003. Integrability of Lie brackets, {\em Ann.of Math}. \textbf{157}: 575-620.

\bibitem{CA94}
Connes A 1994. \emph{Noncommutative geometry}. Academic Press: New York.

\bibitem{CR-LL63}
Croisot, R. and Lesieur, L. 1963. \emph{Alg\`ebre noeth\'erienne non-commutative.},
Gauthier-Villard: Paris.

\bibitem{CRL94}
Crole, R.L., 1994, {\em Categories for Types}, Cambridge: Cambridge University Press.

\bibitem{CJ-LJ91}
Couture, J. \& Lambek, J., 1991, {\em Philosophical Reflections on the Foundations of Mathematics}, Erkenntnis, 34, 2, 187--209.

\bibitem{DJ-ALEX60-71}
Dieudonn\'e, J. \& Grothendieck, A., 1960, [1971], \'El\'ements de G\'eom\'etrie Alg\'ebrique, Berlin: Springer-Verlag.

\bibitem{Dirac30}
Dirac, P. A. M., 1930, {\em The Principles of Quantum Mechanics}, Oxford: Clarendon
Press.

\bibitem{Dirac33}
Dirac, P. A. M., 1933, {\em The Lagrangian in Quantum Mechanics}, Physikalische
Zeitschrift der Sowietunion, \textbf{3}: 64-72.

\bibitem{Dirac43}
Dirac, P. A. M.,, 1943, {\em Quantum Electrodynamics}, Communications of the Dublin
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\bibitem{Dixmier}
Dixmier, J., 1981, Von Neumann Algebras, Amsterdam: North-Holland Publishing
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\bibitem{EC}
Ehresmann, C.: 1965, \emph{Cat\'egories et Structures}, Dunod, Paris.

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Ehresmann, C.: 1966, Trends Toward Unity in Mathematics.,
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Ehresmann, C.: 1959, Cat\'egories topologiques et cat\'egories
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\bibitem{EA-VJP87}
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.

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\bibitem{EACV2}
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a model of Rosen's Organisms, \emph{Axiomathes} \textbf{16} (1--2): 13-50.

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Eilenberg, S. \& MacLane, S., 1942, "Group Extensions and Homology", Annals of Mathematics, 43, 757--831.

\bibitem{ES-SN52}
Eilenberg, S. \& Steenrod, N., 1952, Foundations of Algebraic Topology, Princeton: Princeton University Press.

\bibitem{ES60}
Eilenberg, S.: 1960. Abstract description of some basic functors., J. Indian Math.Soc., \textbf{24} :221-234.

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\bibitem{ED88}
Ellerman, D., 1988, "Category Theory and Concrete Universals", Synthese, 28, 409--429.

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\bibitem{FS77}
Feferman, S., 1977. Categorical Foundations and Foundations of Category Theory, in \emph{Logic, Foundations of Mathematics and Computability}, R. Butts (ed.), Reidel, 149--169.

\bibitem{Fell}
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\end{document}