000 | 03630nam a22005055i 4500 | ||
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001 | 978-3-540-36360-6 | ||
003 | DE-He213 | ||
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007 | cr nn 008mamaa | ||
008 | 100301s2006 gw | s |||| 0|eng d | ||
020 |
_a9783540363606 _9978-3-540-36360-6 |
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_a10.1007/3-540-36359-9 _2doi |
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_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. |
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300 |
_aXII, 225 p. 3 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1890 |
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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. |
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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 | |
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_iPrinted edition: _z9783540826682 |
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_iPrinted edition: _z9783540363590 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1890 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/3-540-36359-9 |
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