Singular Coverings of Toposes

The self-contained theory of certain singular coverings of toposes called complete spreads, that is presented in this volume, is a field of interest to topologists working in knot theory, as well as to various categorists. It extends the complete spreads in topology due to R. H. Fox (1957) but, unli...

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Главные авторы: Bunge, Marta, Funk, Jonathon (Автор)
Формат: Livre numérique
Язык:Anglais
Опубликовано: Berlin, Heidelberg : Springer Berlin Heidelberg [20..].
Cham : Springer Nature
Редактирование:1st ed. 2006.
Серии:Lecture notes in mathematics 1890
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Примечание: L'impression du document génère 237 p.
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Edition sous un autre format:• Singular coverings of toposes, M. Bunge, J. Funk, Berlin, Springer, 2006, 1 vol. (XII-225 p.), Lecture notes in mathematics, 3-540-36359-9
• Singular Coverings of Toposes, Texte imprimé, 9783540826682
• Singular coverings of toposes, M. Bunge, J. Funk, Berlin, Springer, 2006, 1 vol. (XII-225 p.), Lecture notes in mathematics, 3-540-36359-9
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505 1 |a Distributions and Complete Spreads Lawvere Distributions on Toposes Complete Spread Maps of Toposes The Spread and Completeness Conditions An Axiomatic Theory of Complete Spreads Completion KZ-Monads Complete Spreads as Discrete M-fibrations Closed and Linear KZ-Monads Aspects of Distributions and Complete Spreads Lattice-Theoretic Aspects Localic and Algebraic Aspects Topological Aspects 
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520 |a The self-contained theory of certain singular coverings of toposes called complete spreads, that is presented in this volume, is a field of interest to topologists working in knot theory, as well as to various categorists. It extends the complete spreads in topology due to R. H. Fox (1957) but, unlike the classical theory, it emphasizes an unexpected connection with topos distributions in the sense of F. W. Lawvere (1983). The constructions, though often motivated by classical theories, are sometimes quite different from them. Special classes of distributions and of complete spreads, inspired respectively by functional analysis and topology, are studied. Among the former are the probability distributions; the branched coverings are singled out amongst the latter. This volume may also be used as a textbook for an advanced one-year graduate course introducing topos theory with an emphasis on geometric applications. Throughout the authors emphasize open problems. Several routine proofs are left as exercises, but also as exercises the reader will find open questions for possible future work in a variety of topics in mathematics that can profit from a categorical approach 
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