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Singular Coverings of Toposes / by Marta Bunge, Jonathon Funk.
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2379,2381-2383 2385,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Bunge, M. (Marta), author.
- Funk, J. (Jonathon), author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 1890.
- Lecture Notes in Mathematics, 0075-8434 ; 1890
- Language:
- English
- Subjects (All):
- Algebra.
- Cell aggregation--Mathematics.
- Cell aggregation.
- Category Theory, Homological Algebra.
- Manifolds and Cell Complexes (incl. Diff.Topology).
- Order, Lattices, Ordered Algebraic Structures.
- Local Subjects:
- Category Theory, Homological Algebra.
- Manifolds and Cell Complexes (incl. Diff.Topology).
- Order, Lattices, Ordered Algebraic Structures.
- Physical Description:
- 1 online resource (XII, 225 pages 3 illustrations).
- Contained In:
- Springer eBooks
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
- System Details:
- text file PDF
- Summary:
- 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.
- Contents:
- 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.
- Other Format:
- Printed edition:
- ISBN:
- 9783540363606
- Access Restriction:
- Restricted for use by site license.
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