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001 978-3-540-36360-6
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005 20190213151257.0
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020 _a9783540363606
_9978-3-540-36360-6
024 7 _a10.1007/3-540-36359-9
_2doi
050 4 _aQA169
072 7 _aPBC
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBC
_2thema
072 7 _aPBF
_2thema
082 0 4 _a512.6
_223
100 1 _aBunge, Marta.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSingular Coverings of Toposes
_h[electronic resource] /
_cby Marta Bunge, Jonathon Funk.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXII, 225 p. 3 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1890
505 0 _aDistributions 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.
520 _aThe 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.
650 0 _aAlgebra.
650 0 _aCell aggregation
_xMathematics.
650 1 4 _aCategory Theory, Homological Algebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11035
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_0http://scigraph.springernature.com/things/product-market-codes/M28027
650 2 4 _aOrder, Lattices, Ordered Algebraic Structures.
_0http://scigraph.springernature.com/things/product-market-codes/M11124
700 1 _aFunk, Jonathon.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540826682
776 0 8 _iPrinted edition:
_z9783540363590
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1890
856 4 0 _uhttps://doi.org/10.1007/3-540-36359-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10123
_d10123