PlanetPhysics/Bibliography for Axiomatics and Mathematical Physics Foundations in Categories
A Bibliography for Axiomatic Theories and Categorical Foundations of Mathematical Physics and Mathematics edit
\subsubsection{a. Foundations of Mathematics, Logics and Formal Logics: Axiomatics, Categories, Topoi and Higher Dimensional Algebra}
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[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112][113][114][115][116][117][118][119][120][121][122][123][124][125][126][127][128][129][130][131][132][133][134][135][136][137][138][139][140][141][142][143][144][145][146][147][148][149][150][151][152][153][154][155][156][157][158][156][159][160][161][162][163][164][165][166][167][168][169][170][171][172][173][174][175][176][177][178][179][180][181][182][183][184][185][186][187][188][189][190][191][192][193][194][195][196][197][198][199][200][201][202][203][204][205][206][207][208][209][210][211][212][213]
References edit
- ↑ Awodey, S. 1996. "Structure in Mathematics and Logic: A Categorical Perspective.", Philosophia Mathematica , 3, 209--237.
- ↑ Awodey, S., 2006, Category Theory , Oxford: Clarendon Press.
- ↑ Baez, J. and Dolan, J., 1998a, Higher-Dimensional Algebra III. -Categories and the Algebra of Opetopes, Advances in Mathematics , 135: 145--206.
- ↑ Baez, J. and Dolan, J., 1998b, "Categorification", Higher Category Theory, Contemporary Mathematics , 230, Providence: AMS, 1--36.
- ↑ 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., Axiomathes , 16 Nos. 1-2: 65-122.
- ↑ Baianu, I.C. and D. Scripcariu: 1973, On Adjoint Dynamical Systems. Bulletin of Mathematical Biophysics , 35 (4): 475-486.
- ↑ 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, Preprint of Report .
- ↑ Barr, M. and C.~Wells. Toposes, Triples and Theories . Montreal: McGill University, 2000.
- ↑ Barr, M. and 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.
- ↑ Blass, A. and Scedrov, A., 1983, Classifying Topoi and Finite Forcing , Journal of Pure and Applied Algebra, 28, 111--140.
- ↑ Blass, A. and Scedrov, A., 1989, Freyd's Model for the Independence of the Axiom of Choice, Providence: AMS.
- ↑ Blass, A. and 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. and Scott, P., 2004, Category Theory for Linear Logicians., in Linear Logic in Computer Science
- ↑ 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., Theory and Applications of Categories 10 , 71-93.
- ↑ Brown, R. and Spencer, C.B.: 1976, Double groupoids and crossed modules, Cah. Top. G\'{e om. Diff.} 17 , 343-362.
- ↑ 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.
- ↑ Ronald Brown et al.: Non-Abelian Algebraic Topology, vols. I and II. 2010, 620 pages with Index. (March 4, 2010-in press: Springer): Nonabelian Algebraic Topology:filtered spaces, crossed complexes, cubical higher homotopy groupoids
- ↑ Buchsbaum, D. A.: 1955, Exact categories and duality., Trans. Amer. Math. Soc. 80 : 1-34.
- ↑ Bunge, M. and S. Lack: 2003, Van Kampen theorems for toposes, Adv. in Math. 179 , 291-317.
- ↑ 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.
- ↑ 27.0 27.1
Ehresmann, C.: 1965, Cat\'egories et Structures , Dunod, Paris.
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\subsubsection{b. Universal Algebra, Classes of Algebraic Structures and Homology; Abelian and Non-Abelian theories; Algebraic geometry and Noncommutative Geometry}.
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