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Classifying Spaces and Classifying Topoi

  • Authors
  • Izak¬†Moerdijk

Part of the Lecture Notes in Mathematics book series (LNM, volume 1616)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Izak Moerdijk
    Pages 1-4
  3. Izak Moerdijk
    Pages 5-19
  4. Izak Moerdijk
    Pages 21-55
  5. Izak Moerdijk
    Pages 57-76
  6. Izak Moerdijk
    Pages 77-88
  7. Back Matter
    Pages 89-94

About this book

Introduction

This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival- ence is constructed between the classifying space and the classifying topos of any small (topological) category. Topos theory is then applied to give an answer to the question of what structures are classified by "classifying" spaces.
The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory.

Keywords

Algebraic topology Homotopy algebra sheaves topology

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0094441
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-60319-1
  • Online ISBN 978-3-540-44912-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site