Talk:PlanetPhysics/Bibliography for Quantum Algebraic Topology and Categories

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\begin{document}

 \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 \htmladdnormallink{Quantum Algebraic Topology}{http://planetphysics.us/encyclopedia/TriangulationMethodsForQuantizedSpacetimes2.html}. A more extensive bibliography on \emph{\htmladdnormallink{category theory}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html}} can be found on the web at the
\htmladdnormallink{Plato, Stanford Encyclopedia of Philosophy web site}{http://plato.stanford.edu/entries/category-theory/}.


\begin{thebibliography}{999}

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Auslander, M. 1965. Coherent Functors. \emph{Proc. Conf. Cat. Algebra, La Jolla},
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\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, {\em History and Philosophy of Logic}, 23, 2, 77-94.

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

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

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Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes.,
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\bibitem{BAJ-DJ97}
Baez, J., 1997, ``An Introduction to n-Categories'',
{\em Category Theory and Computer Science}, Lecture Notes in Computer Science, 1290, Berlin: Springer-Verlag, 1--33.

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

\bibitem{ICB4}
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Baianu, I.C.: 1973, Some Algebraic Properties of \emph{\textbf{(M,R)}} -- Systems. \emph{Bulletin of Mathematical Biophysics} \textbf{35}, 213-217.

\bibitem{ICBm2}
Baianu, I.C. and M. Marinescu: 1974, On A Functorial Construction of \emph{\textbf{(M,R)}}-- Systems. \emph{Revue Roumaine de Mathematiques Pures et Appliquees} \textbf{19}: 388-391.

\bibitem{ICB6}
Baianu, I.C.: 1977, A Logical Model of Genetic Activities in \L{}ukasiewicz Algebras: The Non-linear Theory. \emph{Bulletin of Mathematical Biology},
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Baianu, I. C.: 1983, Natural Transformation Models in Molecular
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\bibitem{ICB-HG-EO84}
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\bibitem{ICB2}
Baianu, I.C.: 1984, A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Networks, \emph{FASEB Proceedings} \textbf{43}, 917.

\bibitem{ICB87a}
Baianu, I. C.: 1986--1987a, Computer Models and Automata Theory in Biology and Medicine., in M. Witten (ed.),
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\bibitem{ICB87b}
Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures, in \emph{Proceed. Relational Biology Symp.}
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\bibitem{ICB2004a}
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.

\bibitem{ICB04b}
Baianu, I.C.: 2004b \L{}ukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamics).
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\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{Abstract and Preprint of Report}{http://fs512.fshn.uiuc.edu/QAuto.pdf}.

\bibitem{ICB8}
Baianu, I.C.: 2004a, Quantum Nano--Automata (QNA): Microphysical Measurements with Microphysical QNA Instruments,
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\bibitem{ICB9}
Baianu, I. C.: 2004b, Quantum Interactomics and Cancer Mechanisms,
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\bibitem{ICB10}
Baianu, I. C.: 2006, Robert Rosen's Work and Complex Systems Biology, \emph{Axiomathes} \textbf{16}(1--2):25--34.


\bibitem{Bgb2}
Baianu, I. C., Brown, R. and J. F. Glazebrook: 2006, Quantum Algebraic Topology and Field Theories.
\htmladdnormallink{Preprint}{http://fs512.fshn.uiuc.edu/QAT.pdf}


\bibitem{ICB2k8}
Baianu, I.C.: 2008, Translational Genomics and Human Cancer Interactomics, (invited Review, submitted in November 2007 to \emph{Translational Oncogenomics}).


\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{Bbg3}
Baianu, I.C., R. Brown and J.F. Glazebrook. : 2007a, Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness, \emph{Axiomathes}, \textbf{17}: 35-168.

\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", Advances in Mathematics, 136, 39--103.

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

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

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

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

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

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

\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}
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\bibitem{BASA92}
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\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}
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\bibitem{Borceux94}
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\bibitem{Bourbaki1}
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\bibitem{BHR2}
Brown, R., Higgins, P. J. and R. Sivera,: 2007a, \emph{Non-Abelian
Algebraic Topology}, in preparation.\\
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\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.)
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Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed
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\bibitem{BDA55}
Buchsbaum, D. A.: 1955, Exact categories and duality., Trans. Amer. Math. Soc. \textbf{80}: 1-34.

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

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

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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.

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Lawvere, F. W., 1969b, ``Adjointness in Foundations.'', Dialectica, 23, 281--295.

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Lawvere, F. W., 1970, ``Equality in Hyper doctrines and Comprehension Schema as an Adjoint Functor", Applications of Categorical Algebra, Providence: AMS, 1-14.

\bibitem{LT271}
Lawvere, F. W., 1971, ``Quantifiers and Sheaves.'', Actes du Congr\'es International des
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\bibitem{LFW72}
Lawvere, F. W., 1972, ``Introduction.'', Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics, 274, Springer-Verlag, 1--12.

\bibitem{LFW75}
Lawvere, F. W., 1975, ``Continuously Variable Sets: Algebraic Geometry = Geometric Logic.'', Proceedings of the Logic Colloquium Bristol 1973, Amsterdam: North Holland, 135--153.

\bibitem{LFW76}
Lawvere, F. W., 1976, ``Variable Quantities and Variable Structures in Topoi.'', Algebra, Topology, and Category Theory, New York: Academic Press, 101--131.

\bibitem{LFW97}
Lawvere, F. W. \& Schanuel, S., 1997, Conceptual Mathematics: A First Introduction to Categories, Cambridge: Cambridge University Press.

\bibitem{LFW66}
Lawvere, F. W.: 1966, The Category of Categories as a Foundation for Mathematics., in
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\bibitem{LFW63}
Lawvere, F. W.: 1963, Functorial Semantics of Algebraic Theories,
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\bibitem{LFW69}
Lawvere, F. W.: 1969, \emph{Closed Cartesian Categories}., Lecture held as a guest of the
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\bibitem{LFW92}
Lawvere, F. W., 1992, ``Categories of Space and of Quantity.'', The Space of Mathematics, Foundations of Communication and Cognition, Berlin: De Gruyter, 14--30.

\bibitem{LFW94a}
Lawvere, F. W., 1994a, ``Cohesive Toposes and Cantor's lauter Ensein.'', Philosophia Mathematica, 2, 1, 5--15.

\bibitem{LFW94b}
Lawvere, F. W., 1994b, ``Tools for the Advancement of Objective Logic: Closed Categories and Toposes.'', The Logical Foundations of Cognition, Vancouver Studies in Cognitive Science, 4, Oxford: Oxford University Press, 43--56.

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Lawvere, F. W., 2000, ``Comments on the Development of Topos Theory.'', Development of Mathematics 1950-2000, Basel: Birkh\"auser, 715--734.

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Lawvere, F. W., 2002, ``Categorical Algebra for Continuum Micro Physics.'', Journal of Pure and Applied Algebra, 175, no. 1--3, 267--287.

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MacLane, S., 1996, Structure in Mathematics. Mathematical Structuralism., Philosophia Mathematica, 4, 2, 174-183.

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MacLane, S., 1997, Categories for the Working Mathematician, 2nd edition, New York: Springer-Verlag.

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MacLane, S., 1997, Categorical Foundations of the Protean Character of Mathematics., Philosophy of Mathematics Today, Dordrecht: Kluwer, 117--122.

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Makkai, M., 1998, ``Towards a Categorical Foundation of Mathematics.'', Lecture Notes in Logic, 11, Berlin: Springer, 153--190.

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Makkai, M., 1999, ``On Structuralism in Mathematics, Language, Logic and Concepts.'', Cambridge: MIT Press, 43--66.

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\end{document}