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categorical physics
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This is a relatively new area in mathematical and theoretical physics that is concerned with category theory applications to physics, especially non-Abelian categories and non-Abelian algebraic topology concepts and results in mathematical physics and physical mathematics. Applications range from QFT, AQFT, non-Abelian gauge theories and quantum gravity to complex systems, categorical dynamics, complex categorical dynamics, mathematical biophysics and relational biology. Other applications are related to graph theory approaches to Quantum Chemistry.
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- Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems. Bulletin of Mathematical Biophysics, 35(4): 475-486.
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- Gabriel, P. and N. Popescu: 1964, Caractérisation des catégories abéliennes avec générateurs et limites inductives. , CRAS Paris 258: 4188-4191.
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- Galli, A. & Reyes, G. & Sagastume, M., 2000, Completeness Theorems via the Double Dual Functor, Studia Logica, 64, no. 1: 61–81.
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- Kan, D. M., 1958, Adjoint Functors, Transactions of the American Mathematical Society 87, 294-329.
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- H. Krips : Measurement in Quantum Theory, The Stanford Encyclopedia of Philosophy (Winter 1999 Edition), Edward N. Zalta (ed.)
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- Landsman, N. P. : Compact quantum groupoids, (at arXiv:math� @ Tph/9912006).
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- Lawvere, F. W., 1964, An Elementary Theory of the Category of Sets, Proceedings of the National Academy of Sciences U.S.A., 52, 1506–1511.
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- Lawvere, F. W., 1992, Categories of Space and of Quantity, The Space of Mathematics, Foundations of Communication and Cognition, Berlin: De Gruyter, 14-30.
- 41
- Lawvere, F. W., 2002, Categorical Algebra for Continuum Micro-Physics, Journal of Pure and Applied Algebra, 175, no. 1–3, 267–287.
- 42
- Li, M. and P. Vitanyi: 1997, An introduction to Kolmogorov Complexity and its Applications, Springer Verlag: New York.
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"categorical physics" is owned by bci1.
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See Also: category, 2-category, groupoid, ultracomplex systems and categorical dynamics, alternative definition of category
Other names: |
non-Abelian algebraic topology applied to physics |
Also defines: |
categorification, ``categorification'' |
Keywords: |
category theory applications to physics |
Cross-references: graph, relational biology, systems, quantum gravity, non-Abelian, AQFT, QFT, mathematical physics and physical mathematics, concepts, non-Abelian algebraic topology, non-Abelian categories, theoretical physics
This is version 11 of categorical physics, born on 2008-12-24, modified 2010-03-05.
Object id is 350, canonical name is CategoricalPhysics.
Accessed 1112 times total.
Classification:
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Pending Errata and Addenda
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