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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edit[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}.
References
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