Talk:PlanetPhysics/Bibliography for Axiomatics and Mathematical Physics Foundations in Categories

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\begin{document}

 \subsection{A Bibliography for Axiomatic Theories and Categorical Foundations of Mathematical Physics and Mathematics}


\subsubsection{a. Foundations of Mathematics, Logics and
Formal Logics:
Axiomatics, Categories, Topoi and
\htmladdnormallink{Higher Dimensional Algebra}{http://planetphysics.us/encyclopedia/HigherDimensionalAlgebra2.html}}

\begin{thebibliography}{99}

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

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

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

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

\bibitem{BBGG1}
Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006, 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{ICBDS73}
Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems.
\emph{Bulletin of Mathematical Biophysics}, \textbf{35}(4): 475-486.

\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,
\emph{Preprint of Report}.

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

\bibitem{BM-CW99}
Barr, M. and Wells, C. 1999.\emph{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., 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{BA-SA83}
Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111--140.

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

\bibitem{BASA92}
Blass, A. and Scedrov, A., 1992. Complete Topoi Representing Models of Set Theory, 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. and Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science

\bibitem{BP2k3}
Brown R. and T. Porter: 2003, Category theory and higher dimensional algebra: potential descriptive tools in neuroscience, In: {\em Proceedings of the International Conference on Theoretical Neurobiology}, Delhi, February 2003, edited by Nandini Singh, National Brain Research Centre, {\em Conference Proceedings} \textbf{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-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{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{RBPGV}
Ronald Brown et al.: Non-Abelian Algebraic Topology, vols. I and II. 2010, 620 pages with Index. (March 4, 2010-in press: Springer): \htmladdnormallink{Nonabelian Algebraic Topology:filtered spaces, crossed complexes, cubical higher homotopy groupoids}{http://www.bangor.ac.uk/~mas010/rbrsbookb-e040310.pdf}

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

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

\bibitem{BM84}
Bunge, M., 1984, Toposes in Logic and Logic in Toposes, {\em 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{EC}
Ehresmann, C.: 1965, \emph{Cat\'egories et Structures}, Dunod, Paris.

\bibitem{EC}
Ehresmann, C.: 1966, Trends Toward Unity in Mathematics., \emph{Cahiers de Topologie et Geometrie Differentielle}
\textbf{8}: 1-7.

\end{thebibliography}


\subsubsection{b. Universal Algebra, Classes of Algebraic Structures and Homology; Abelian and
Non-Abelian theories; Algebraic
geometry and \htmladdnormallink{Noncommutative Geometry}{http://planetphysics.us/encyclopedia/NoncommutativeGeometry.html}}.

\begin{thebibliography}{199}

\bibitem{BHR2}
Brown, R., Higgins, P. J. and R. Sivera,: 2007, \emph{Non-Abelian Algebraic Topology},
\htmladdnormallink{vol.I pdf doc.}{http://www.bangor.ac.uk/~mas010/nonab-t/partI010604.pdf};
\htmladdnormallink{Review of Part I and full contents PDF doc.}{http://planetmath.org/?op=getobj&from=lec&id=75}

\bibitem{RB2k8}
R. Brown. 2008. {\em Higher Dimensional Algebra Preprint as pdf and ps docs. at arXiv:math/0212274v6 [math.AT]}

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

\bibitem{CH-ES56}
Cartan, H. and Eilenberg, S. 1956. {\em Homological Algebra}, Princeton Univ. Press: Pinceton.

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

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

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

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

\bibitem{Dixmier}
Dixmier, J., 1981, Von Neumann Algebras, Amsterdam: North-Holland Publishing Company. [First published in French in 1957: Les Algebres d'Operateurs dans l'Espace Hilbertien, Paris: Gauthier--Villars.]

\bibitem{Durdevich1}
M. Durdevich : Geometry of quantum principal bundles I, Commun. Math. Phys. \textbf{175} (3) (1996), 457--521.

\bibitem{Durdevich2}
M. Durdevich : Geometry of quantum principal bundles II, Rev.Math. Phys. \textbf{9} (5) (1997), 531-607.

\bibitem{Eh-pseudo}
Ehresmann, C.: 1952, Structures locales et structures infinit\'esimales, \emph{C.R.A.S.} Paris \textbf{274}: 587-589.

\bibitem{Eh}
Ehresmann, C.: 1959, Cat\'egories topologiques et cat\'egories diff\'erentiables, \emph{Coll. G\'eom. Diff. Glob.} Bruxelles, pp.137-150.

\bibitem{Eh-quintettes}
Ehresmann, C.:1963, Cat\'egories doubles des quintettes: applications covariantes , \emph{C.R.A.S. Paris}, \textbf{256}: 1891--1894.

\bibitem{Eh-Oe}
Ehresmann, C.: 1984, \emph{Oeuvres compl\`etes et comment\'ees: Amiens, 1980-84}, edited and commented by Andr\'ee Ehresmann.

\bibitem{EML1}
Eilenberg, S. and S. Mac Lane.: 1942, Natural Isomorphisms in Group Theory., \emph{American Mathematical Society 43}: 757-831.

\bibitem{EL}
Eilenberg, S. and S. Mac Lane: 1945, The General Theory of Natural Equivalences, \emph{Transactions of the American Mathematical Society} \textbf{58}: 231-294.

\bibitem{ES-CH56}
Eilenberg, S. \& Cartan, H., 1956, {\em Homological Algebra}, Princeton: Princeton University Press.

\bibitem{ES-MCLS42}
Eilenberg, S. \& MacLane, S., 1942, Group Extensions and Homology, {\em Annals of Mathematics}, 43, 757--831.

\bibitem{ES-SN52}
Eilenberg, S. \& Steenrod, N., 1952, {\em 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.

\bibitem{S.Eilenberg}
S.Eilenberg. Relations between Homology and Homotopy Groups. {\em Proc.Natl.Acad.Sci.USA} (1966),v:10--14.

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

\bibitem{ETH}
Ezawa,Z.F., G. Tsitsishvilli and K. Hasebe : Noncommutative geometry, extended $W_{\infty}$ algebra and Grassmannian solitons in multicomponent Hall systems, (at arXiv:hep--th/0209198).

\bibitem{FP2k2}
Freyd, P., 2002, Cartesian Logic, {\em Theoretical Computer Science}, 278, no. 1--2, 3--21.

\bibitem{FP-FH-SA87}
Freyd, P., Friedman, H. \& Scedrov, A., 1987, Lindembaum Algebras of Intuitionistic Theories and Free Categories, {\em Annals of Pure and Applied Logic}, 35, 2, 167--172.

\bibitem{Gablot}
Gablot, R. 1971. Sur deux classes de cat\'{e}gories de Grothendieck. {\em Thesis}, Univ. de Lille.

\bibitem{Gabriel1}
Gabriel, P.: 1962, Des cat\'egories ab\'eliennes, \emph{Bull. Soc. Math. France} \textbf{90}: 323-448.

\bibitem{Gabriel2}
Gabriel, P. and M.Zisman:. 1967: \emph{Category of fractions and homotopy theory}, \emph{Ergebnesse der math.} Springer: Berlin.

\bibitem{GabrielNP}
Gabriel, P. and N. Popescu: 1964, Caract\'{e}risation des cat\'egories ab\'eliennes
avec g\'{e}n\'{e}rateurs et limites inductives. , \emph{CRAS Paris} \textbf{258}: 4188-4191.

\bibitem{GA-RG-SM2k}
Galli, A. \& Reyes, G. \& Sagastume, M., 2000, Completeness Theorems via the Double Dual Functor,
{\em Studia Logica}, \textbf{64}, no. 1: 61--81.

\bibitem{GN}
Gelfan'd, I. and Naimark, M., 1943, On the Imbedding of Normed Rings into the Ring of Operators in Hilbert Space, Recueil Math\'ematique [Matematicheskii Sbornik] Nouvelle S\'erie, 12 [54]: 197--213. [Reprinted in C*--algebras:
1943--1993, in the series Contemporary Mathematics, 167, Providence, R.I.: American Mathematical Society, 1994.]

\bibitem{GS-ZM2K2}
Ghilardi, S. \& Zawadowski, M., 2002, {\em Sheaves, Games \& Model Completions: A Categorical Approach to Nonclassical Propositional Logics}, Dordrecht: Kluwer.

\bibitem{gs89}
Ghilardi, S., 1989, Presheaf Semantics and Independence Results for some Non-classical first-order logics,
{\em Archive for Mathematical Logic}, 29, no. 2, 125--136.

\bibitem{Gob68}
Goblot, R., 1968, Cat\'egories modulaires , {\em C. R. Acad. Sci. Paris, S\'erie A.}, \textbf{267}: 381--383.

\bibitem{Gob71}
Goblot, R., 1971, Sur deux classes de cat\'egories de Grothendieck, {\em Th\`ese.}, Univ. Lille, 1971.

\bibitem{GR79}
Goldblatt, R., 1979, Topoi: The Categorical Analysis of Logic, Studies in logic and the foundations of mathematics, Amsterdam: Elsevier North-Holland Publ. Comp.

\bibitem{Goldie}
Goldie, A. W., 1964, Localization in non-commutative noetherian rings, {\em J.Algebra}, \textbf{1}: 286-297.

\bibitem{Godement}
Godement,R. 1958. Th\'{e}orie des faisceaux. Hermann: Paris.

\bibitem{GRAY65}
Gray, C. W.: 1965. Sheaves with values in a category.,\emph {Topology}, 3: 1-18.

\bibitem{Alex71}
Grothendieck, A.: 1971, Rev\^{e}tements \'Etales et Groupe Fondamental (SGA1),
chapter VI: Cat\'egories fibr\'ees et descente, \emph{Lecture Notes in Math.}
\textbf{224}, Springer--Verlag: Berlin.

\bibitem{Alex57}
Grothendieck, A.: 1957, Sur quelque point d-alg\`{e}bre homologique. , \emph{Tohoku Math. J.}, \textbf{9:} 119-121.

\bibitem{Alex3}
Grothendieck, A. and J. Dieudon\'{e}.: 1960, El\'{e}ments de geometrie alg\'{e}brique., \emph{Publ. Inst. des Hautes Etudes de Science}, \textbf{4}.

\bibitem{ALEXsem}
Grothendieck, A. et al., S\'eminaire de G\'eom\'etrie Alg\'ebrique, Vol. 1--7, Berlin: Springer-Verlag.

\bibitem{HKK}
Hardie, K.A. K.H. Kamps and R.W. Kieboom, A homotopy 2-groupoid of a Hausdorff space, {\em Applied Cat. Structures} 8 (2000), 209-234.

\bibitem{HWS82}
Hatcher, W. S., 1982, {\em The Logical Foundations of Mathematics}, Oxford: Pergamon Press.

\bibitem{Heller58}
Heller, A. :1958, Homological algebra in Abelian categories., \emph{Ann. of Math.}
\textbf{68}: 484-525.

\bibitem{HellerRowe62}
Heller, A. and K. A. Rowe.:1962, On the category of sheaves., \emph{Amer J. Math.}
\textbf{84}: 205-216.

\bibitem{HG2k3}
Hellman, G., 2003, "Does Category Theory Provide a Framework for Mathematical Structuralism?", Philosophia Mathematica, 11, 2, 129--157.

\bibitem{HC-MM-PJ2K}
Hermida, C. \& Makkai, M. \& Power, J., 2000, On Weak Higher-dimensional Categories I, Journal of Pure and Applied Algebra, 154, no. 1-3, 221--246.

\bibitem{HC-MM-PI2K1}
Hermida, C. \& Makkai, M. \& Power, J., 2001, On Weak Higher-dimensional Categories II, Journal of Pure and Applied Algebra, 157, no. 2-3, 247--277.

\bibitem{HC-MM-PI2K2}
Hermida, C. \& Makkai, M. \& Power, J., 2002, On Weak Higher-dimensional Categories III, Journal of Pure and Applied Algebra, 166, no. 1-2, 83--104.

\bibitem{HPJbook}
Higgins, P. J.: 2005, \emph{Categories and groupoids}, Van Nostrand Mathematical Studies: 32, (1971); \emph{Reprints in
Theory and Applications of Categories}, No. 7: 1-195.

\bibitem{HPJ2k5}
Higgins, Philip J. Thin elements and commutative shells in cubical $\omega$-categories. Theory Appl. Categ. 14 (2005), No. 4, 60--74 (electronic). msc: 18D05.

\bibitem{HJ-RE-RG90}
Hyland, J.M.E. \& Robinson, E.P. \& Rosolini, G., 1990, The Discrete Objects in the Effective Topos,
{\em Proceedings of the London Mathematical Society} (3), 60, no. 1, 1--36.

\bibitem{HJME82}
Hyland, J.M.E., 1982, The Effective Topos, {\em Studies in Logic and the Foundations of Mathematics}, 110, Amsterdam: North Holland, 165--216.

\bibitem{HJME88}
Hyland, J. M..E., 1988, A Small Complete Category, {\em Annals of Pure and Applied Logic}, 40, no. 2, 135--165.

\bibitem{HJME91}
Hyland, J. M .E., 1991, First Steps in Synthetic Domain Theory, {\em Category Theory (Como 1990)}, Lecture Notes in Mathematics, 1488, Berlin: Springer, 131-156.

\bibitem{HJME2K2}
Hyland, J. M.E., 2002, Proof Theory in the Abstract, {\em Annals of Pure and Applied Logic}, 114, no. 1--3, 43--78.

\bibitem{E.Hurewicz}
E.Hurewicz. CW Complexes., {\em Trans AMS}.1955.

\bibitem{JB99}
Jacobs, B., 1999, Categorical Logic and Type Theory, Amsterdam: North Holland.

\bibitem{JPT77}
Johnstone, P. T., 1977, Topos Theory, New York: Academic Press.

\bibitem{JPT79A}
Johnstone, P. T., 1979a, {\em Conditions Related to De Morgan's Law, Applications of Sheaves}, Lecture Notes in Mathematics, 753, Berlin: Springer, 479--491.

\bibitem{JPT81}
Johnstone, P. T., 1981, Tychonoff's Theorem without the Axiom of Choice,
{\em Fundamenta Mathematicae}, 113, no. 1, 21--35.

\bibitem{JPT52}
Johnstone, P. T., 1982, {\em Stone Spaces}, Cambridge:Cambridge University Press.

\bibitem{JPT85}
Johnstone, P. T., 1985, How General is a Generalized Space?, {\em Aspects of Topology}, Cambridge: Cambridge University Press, 77--111.

\bibitem{JAMI95}
Joyal, A. \& Moerdijk, I., 1995, {\em Algebraic Set Theory}, Cambridge: Cambridge University Press.

\bibitem{kampen1-1933}
Van Kampen, E. H.: 1933, On the Connection Between the Fundamental
Groups of some Related Spaces, \emph{Amer. J. Math.} \textbf{55}: 261-267

\bibitem{KDM58}
Kan, D. M., 1958, Adjoint Functors, {\em Transactions of the American Mathematical Society} 87, 294-329.

\bibitem{Kleisli62}
Kleisli, H.: 1962, Homotopy theory in Abelian categories.,{\em Can. J. Math.}, \textbf{14}: 139-169.

\bibitem{KJT70}
Knight, J.T., 1970, On epimorphisms of non-commutative rings., {\em Proc. Cambridge Phil. Soc.},
\textbf{25}: 266-271.

\bibitem{KA81}
Kock, A., 1981, {\em Synthetic Differential Geometry}, London Mathematical Society Lecture Note Series, 51, Cambridge: Cambridge University Press.

\bibitem{KN1}
S. Kobayashi and K. Nomizu : {\em Foundations of Differential Geometry}, Vol I., Wiley Interscience, New York--London 1963.

\bibitem{Krips}
H. Krips : Measurement in Quantum Theory, \emph{The Stanford Encyclopedia of Philosophy} (Winter 1999 Edition),
Edward N. Zalta (ed.),

\bibitem{LTY}
Lam, T. Y., 1966, The category of noetherian modules, {\em Proc. Natl. Acad. Sci. USA}, \textbf{55}: 1038-104.

\bibitem{LJ-SPJ86}
Lambek, J. \& Scott, P.J., 1986, {\em Introduction to Higher Order Categorical Logic}, Cambridge: Cambridge University Press.

\bibitem{LJ68}
Lambek, J., 1968, Deductive Systems and Categories I. Syntactic Calculus and Residuated Categories,
{\em Mathematical Systems Theory}, 2, 287--318.

\bibitem{LJ69}
Lambek, J., 1969, {\em Deductive Systems and Categories II. Standard Constructions and Closed Categories, Category Theory, Homology Theory and their Applications I}, Berlin: Springer, 76--122.

\bibitem{LJ72}
Lambek, J., 1972, {\em Deductive Systems and Categories III. Cartesian Closed Categories, Intuitionistic Propositional Calculus, and Combinatory Logic, Toposes, Algebraic Geometry and Logic}, Lecture Notes in Mathematics, 274, Berlin: Springer, 57--82.

\bibitem{LT89A}
Lambek, J., 1989A, On Some Connections Between Logic and Category Theory, {\em Studia Logica}, 48, 3, 269--278.

\bibitem{LJ89B}
Lambek, J., 1989B, On the Sheaf of Possible Worlds, {\em Categorical Topology and its relation to Analysis, Algebra and Combinatorics}, Teaneck: World Scientific Publishing, 36--53.

\bibitem{LJ94a}
Lambek, J., 1994a, Some Aspects of Categorical Logic, in {\em Logic, Methodology and Philosophy of Science IX, Studies in Logic and the Foundations of Mathematics} \textbf{134}, Amsterdam: North Holland, 69--89.

\bibitem{LJ2k4}
Lambek, J., 2004, What is the world of Mathematics? Provinces of Logic Determined, {\em Annals of Pure and Applied Logic}, \textbf{126}(1-3), 149--158.

\bibitem{LaSc}
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\end{document}