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Singular Coverings of Toposes

  • Marta Bunge
  • Jonathon Funk

Part of the Lecture Notes in Mathematics book series (LNM, volume 1890)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Distributions and Complete Spreads

  3. An Axiomatic Theory of Complete Spreads

    1. Front Matter
      Pages 78-78
    2. Pages 79-97
  4. Aspects of Distributions and Complete Spreads

    1. Front Matter
      Pages 130-130
    2. Pages 189-215
  5. Back Matter
    Pages 217-229

About this book

Introduction

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.

Keywords

2-categories Lattice distributions locales singular coverings toposes

Authors and affiliations

  • Marta Bunge
    • 1
  • Jonathon Funk
    • 2
  1. 1.Department of MathematicsMcGill UniversityMontréalCanada
  2. 2.Department of Computer Science, Mathematics, and PhysicsThe University of the West IndiesBridgetownWest Indies

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-36359-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-36359-0
  • Online ISBN 978-3-540-36360-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site