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＜E-Book＞
Singular Coverings of Toposes / by Marta Bunge, Jonathon Funk
(Lecture Notes in Mathematics. ISSN:16179692 ; 1890)

Edition	1st ed. 2006.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2006
Language	English
Size	XII, 225 p. 3 illus : online resource
Authors	*Bunge, Marta author Funk, Jonathon author SpringerLink (Online service)
Subjects	LCSH:Algebra, Homological LCSH:Manifolds (Mathematics) LCSH:Algebra FREE:Category Theory, Homological Algebra FREE:Manifolds and Cell Complexes FREE:Order, Lattices, Ordered Algebraic Structures
Notes	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 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 HTTP:URL=https://doi.org/10.1007/3-540-36359-9

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