PlanetPhysics/Bibliography for Mathematical Physics Foundations
Bibliography for mathematical physics foundations
editA1. Axiomatics and \htmladdnormallink{categories {http://planetphysics.us/encyclopedia/Cod.html} in the foundations of physics}
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References
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- ↑ 2.0 2.1
Atiyah, M.F. 1956. On the Krull-Schmidt theorem with applications to sheaves.
Bull. Soc. Math. France , 84 : 307--317.
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tag; name "AMF56" defined multiple times with different content - ↑ Awodey, S. \& Butz, C., 2000, Topological Completeness for Higher Order Logic., Journal of Symbolic Logic, 65, 3, 1168--1182.
- ↑ 4.0 4.1
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.
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tag; name "AS-RER2k2" defined multiple times with different content - ↑ Awodey, S., 1996, Structure in Mathematics and Logic: A Categorical Perspective, Philosophia Mathematica , 3: 209--237.
- ↑ Awodey, S., 2004, An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism, Philosophia Mathematica , 12: 54--64.
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- ↑ Baez, J. \& Dolan, J., 1998b, ``Categorification", Higher Category Theory, Contemporary Mathematics, 230, Providence: AMS, 1--36.
- ↑ Baez, J. \& Dolan, J., 2001, From Finite Sets to Feynman Diagrams, in Mathematics Unlimited -- 2001 and Beyond , Berlin: Springer, 29--50.
- ↑ Baez, J., 1997, An Introduction to n-Categories, in Category Theory and Computer Science, Lecture Notes in Computer Science , 1290, Berlin: Springer-Verlag, 1--33.
- ↑ 12.0 12.1
Baianu, I.C.: 1971a, Organismic Supercategories and Qualitative Dynamics of Systems. Ibid. , 33 (3), 339--354.
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tag; name "ICB4" defined multiple times with different content - ↑ Baianu, I.C., H. S. Gutowsky, and E. Oldfield: 1984, Proc. Natl. Acad. Sci. USA , 81 (12): 3713-3717.
- ↑ 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, [\\http://www.ag.uiuc.edu/fs401/QAuto.pdf PDF's of Abstract and Preprint of Report].
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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., Axiomathes , 16 Nos. 1--2: 65--122.
- ↑ Baianu, I.C., R. Brown and J. F. Glazebrook: 2007b, A Non-Abelian, Categorical Ontology of Spacetimes and Quantum Gravity, Axiomathes, 17: 169-225.
- ↑ M.~Barr and C.~Wells. Toposes, Triples and Theories . Montreal: McGill University, 2000.
- ↑ Barr, M. \& Wells, C., 1985, Toposes, Triples and Theories, New York: Springer-Verlag.
- ↑ Barr, M. \& Wells, C., 1999, Category Theory for Computing Science, Montreal: CRM.
- ↑ Batanin, M., 1998, Monoidal Globular Categories as a Natural Environment for the Theory of Weak n-Categories, Advances in Mathematics , 136: 39--103.
- ↑ Bell, J. L., 1981, Category Theory and the Foundations of Mathematics, British Journal for the Philosophy of Science , 32, 349--358.
- ↑ Bell, J. L., 1982, Categories, Toposes and Sets, Synthese , 51, 3, 293--337.
- ↑ Bell, J. L., 1986, From Absolute to Local Mathematics, Synthese , 69, 3, 409--426.
- ↑ Bell, J. L., 1988, Toposes and Local Set Theories: An Introduction, Oxford: Oxford University Press.
- ↑ Birkoff, G. \& Mac Lane, S., 1999, Algebra, 3rd ed., Providence: AMS.
- ↑ Biss, D.K., 2003, Which Functor is the Projective Line?, American Mathematical Monthly , 110, 7, 574--592.
- ↑ Blass, A. \& Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111--140.
- ↑ Blass, A. \& Scedrov, A., 1989, Freyd's Model for the Independence of the Axiom of Choice, Providence: AMS.
- ↑ Blass, A. \& Scedrov, A., 1992, Complete Topoi Representing Models of Set Theory, Annals of Pure and Applied Logic , 57, no. 1, 1--26.
- ↑ Blass, A., 1984, The Interaction Between Category Theory and Set Theory., Mathematical Applications of Category Theory, 30, Providence: AMS, 5--29.
- ↑ Blute, R. \& Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science
- ↑ Borceux, F.: 1994, Handbook of Categorical Algebra , vols: 1--3, in Encyclopedia of Mathematics and its Applications 50 to 52 , Cambridge University Press.
- ↑ Bourbaki, N. 1961 and 1964: Alg\`{e bre commutative.}, in \'{E}l\'{e}ments de Math\'{e}matique., Chs. 1--6., Hermann: Paris.
- ↑ R. Brown: Topology and Groupoids , BookSurge LLC (2006).
- ↑ Brown, R. and G. Janelidze: 2004, Galois theory and a new homotopy double groupoid of a map of spaces, \emph{Applied Categorical Structures} 12 : 63-80.
- ↑ Brown, R., Higgins, P. J. and R. Sivera,: 2007a, \emph{Non-Abelian Algebraic Topology},Vol.I PDF.
- ↑ 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.
- ↑ 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.
- ↑ 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.
- ↑ Brown, R., Hardie, K., Kamps, H. and T. Porter: 2002, The homotopy double groupoid of a Hausdorff space., \emph{Theory and Applications of Categories} 10 , 71-93.
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- ↑ 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.
- ↑ Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, Cah. Top. G\'{e om. Diff.} 17 , 343-362.
- ↑ Brown R, and Porter T (2006) Category theory: an abstract setting for analogy and comparison. In: What is category theory? Advanced studies in mathematics and logic . Polimetrica Publisher, Italy, pp. 257-274.
- ↑ Brown R, Razak Salleh A (1999) Free crossed resolutions of groups and presentations of modules of identities among relations. LMS J. Comput. Math. , 2 : 25--61.
- ↑ 48.0 48.1
Buchsbaum, D. A.: 1955, Exact categories and duality., Trans. Amer. Math. Soc. 80 : 1-34.
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tag; name "BDA55" defined multiple times with different content - ↑ Bucur, I. (1965). Homological Algebra . (orig. title: "Algebra Omologica") Ed. Didactica si Pedagogica: Bucharest.
- ↑ Bucur, I., and Deleanu A. (1968). Introduction to the Theory of Categories and Functors . J.Wiley and Sons: London
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- ↑ Bunge, M., 1984, "Toposes in Logic and Logic in Toposes", Topoi, 3, no. 1, 13-22.
- ↑ Bunge M, Lack S (2003) Van Kampen theorems for toposes. Adv Math , \textbf {179}: 291-317.
- ↑ 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.
- ↑ Butterfield J., Isham C.J. 1998, 1999, 2000-2002, A topos perspective on the Kochen-Specker theorem I-IV, Int J Theor Phys 37(11):2669-2733; 38(3):827-859; 39(6):1413-1436; 41(4): 613-639.
- ↑ Cartan, H. and Eilenberg, S. 1956. Homological Algebra , Princeton Univ. Press: Pinceton.
- ↑ M. Chaician and A. Demichev. 1996. Introduction to Quantum Groups, World Scientific .
- ↑ Chevalley, C. 1946. The theory of Lie groups. Princeton University Press, Princeton NJ
- ↑ Cohen, P.M. 1965. Universal Algebra , Harper and Row: New York, london and Tokyo.
- ↑ M. Crainic and R. Fernandes.2003. Integrability of Lie brackets, Ann.of Math . 157 : 575-620.
- ↑ Connes A 1994. Noncommutative geometry . Academic Press: New York.
- ↑ Croisot, R. and Lesieur, L. 1963. Alg\`ebre noeth\'erienne non-commutative. , Gauthier-Villard: Paris.
- ↑ Crole, R.L., 1994, Categories for Types , Cambridge: Cambridge University Press.
- ↑ Couture, J. \& Lambek, J., 1991, Philosophical Reflections on the Foundations of Mathematics , Erkenntnis, 34, 2, 187--209.
- ↑ Dieudonn\'e, J. \& Grothendieck, A., 1960, [1971], \'El\'ements de G\'eom\'etrie Alg\'ebrique, Berlin: Springer-Verlag.
- ↑ Dirac, P. A. M., 1930, The Principles of Quantum Mechanics , Oxford: Clarendon Press.
- ↑ Dirac, P. A. M., 1933, The Lagrangian in Quantum Mechanics , Physikalische Zeitschrift der Sowietunion, 3 : 64-72.
- ↑ Dirac, P. A. M.,, 1943, Quantum Electrodynamics , Communications of the Dublin Institute for Advanced Studies, A1 : 1-36.
- ↑ 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.]
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- ↑ 73.0 73.1
Ehresmann, C.: 1965, Cat\'egories et Structures , Dunod, Paris.
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tag; name "EC" defined multiple times with different content - ↑ Ehresmann, C.: 1952, Structures locales et structures infinit\'esimales, C.R.A.S. Paris 274 : 587-589.
- ↑ Ehresmann, C.: 1959, Cat\'egories topologiques et cat\'egories diff\'erentiables, Coll. G\'eom. Diff. Glob. Bruxelles, pp.137-150.
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- ↑ Kock, A., 1981, Synthetic Differential Geometry, London Mathematical Society Lecture Note Series, 51, Cambridge: Cambridge University Press.
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