Talk:PlanetPhysics/Algebraic Topology and Applications Bibliography for Category Theory
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This is an extensive, but not intended to be comprehensive, list of relevant, selected references for several areas of both abstract and applied mathematics. A more extensive bibliography on category theory can be found on the
web at:
\htmladdnormallink{Plato, Stanford Encyclopedia of Philosophy web site}{http://plato.stanford.edu/entries/category-theory/}.
\subsection{Literature for the following areas of mathematics:}
\begin{itemize}
\item \htmladdnormallink{algebraic topology}{http://planetphysics.us/encyclopedia/ModuleAlgebraic.html},
\item Theory of \htmladdnormallink{categories}{http://planetphysics.us/encyclopedia/Cod.html}, \htmladdnormallink{functors}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} and \htmladdnormallink{natural transformations}{http://planetphysics.us/encyclopedia/VariableCategory2.html},
\item \htmladdnormallink{Quantum Algebraic Topology}{http://planetphysics.us/encyclopedia/TriangulationMethodsForQuantizedSpacetimes2.html},
\item N-logic \htmladdnormallink{algebraic categories}{http://planetphysics.us/encyclopedia/CategoryOfLogicAlgebras.html},
\item Topoi and \htmladdnormallink{categorical ontology}{http://planetphysics.us/encyclopedia/CategoricalOntology.html} \end{itemize}
\begin{thebibliography}{399}
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Ad\'amek, J.. et al., \emph{Locally Presentable and Accessible Categories.}, Cambridge: Cambridge University Press (1994).
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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, {\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.
\bibitem{AS2k6}
Awodey, S., 2006, {\em Category Theory}, Oxford: Clarendon Press.
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Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. n-Categories and the Algebra of Opetopes.,
{\em Advances in Mathematics}, {\bf 135}, 145--206.
\bibitem{BAJ-DJ98B}
Baez, J. and Dolan, J., 1998b, ``Categorification'', Higher Category Theory, Contemporary Mathematics, 230, Providence: AMS, 1-36.
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Baez, J. and Dolan, J., 2001, ``From Finite Sets to Feynman Diagrams'',
{\em Mathematics Unlimited -- 2001 and Beyond}, Berlin: Springer, 29-50.
\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}
Baianu, I.C.: 1971b, Categories, Functors and Quantum Algebraic
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\bibitem{ICB5}
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.
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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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\bibitem{ICB2}
Baianu, I.C.: 1980a, Natural Transformations of Organismic Structures.,
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\bibitem{ICB2}
Baianu, I. C.: 1983, Natural Transformation Models in Molecular
Biology., in \emph{Proceedings of the SIAM Natl. Meet}., Denver,CO.;
\htmladdnormallink{Eprint at cogprints.org/3675}{http://cogprints.org/3675/1/Naturaltransfmolbionu6.pdf}
\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.),
\emph{Mathematical Models in Medicine}, vol. 7., Ch.11 Pergamon Press, New York, 1513 -1577; URLs:
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and \htmladdnormallink{html Abstract}{http://en.scientificcommons.org/1857371}.
\bibitem{ICB87b}
Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures, in \emph{Proceed. Relational Biology Symp.}
Argentina;
\htmladdnormallink{CERN Preprint No.EXT-2004-067}{http://doc.cern.ch//archive/electronic/other/ext/ext-2004-067.pdf} .
\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,
\emph{CERN Preprint EXT--2004--125}.
\bibitem{ICB9}
Baianu, I. C.: 2004b, Quantum Interactomics and Cancer Mechanisms,
\htmladdnormallink{Preprint 00001978}{http://doc.cern.ch//archive/electronic/other/ext/ext-2004-118.pdf} .
\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}).
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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}
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,
{\em Annals of Pure and Applied Logic} , {\bf 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}
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Brown, R. and G. Janelidze: 2004, Galois theory and a new homotopy
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\bibitem{BHR2}
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
\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.;
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\bibitem{BP2k3}
Brown R. and T. Porter: 2003, Category theory and higher
dimensional algebra: potential descriptive tools in neuroscience, In:
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\end{thebibliography}
Classification:
AMS MSC: 00A15 (General :: General and miscellaneous specific topics :: Bibliographies)
03-00 (Mathematical logic and foundations :: General reference works )
18-00 (Category theory; homological algebra :: General reference works )
18C99 (Category theory; homological algebra :: Categories and theories :: Miscellaneous)
18A05 (Category theory; homological algebra :: General theory of categories and functors :: Definitions, generalizations)
18A30 (Category theory; homological algebra :: General theory of categories and functors :: Limits and colimits )
18A25 (Category theory; homological algebra :: General theory of categories and functors :: Functor categories, comma categories)
18C99 (Category theory; homological algebra :: Categories and theories :: Miscellaneous)
18A40 (Category theory; homological algebra :: General theory of categories and functors :: Adjoint functors )
55U30 (Algebraic topology :: Applied homological algebra and category theory :: Duality)
92B05 (Biology and other natural sciences :: Mathematical biology in general :: General biology and biomathematics)
92B10 (Biology and other natural sciences :: Mathematical biology in general :: Taxonomy, statistics)
92B99 (Biology and other natural sciences :: Mathematical biology in general :: Miscellaneous)
\end{document}