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  • © 1995

Classifying Spaces and Classifying Topoi

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VII
  2. Introduction

    • Izak Moerdijk
    Pages 1-4
  3. Background in topos theory

    • Izak Moerdijk
    Pages 5-19
  4. Classifying topoi

    • Izak Moerdijk
    Pages 21-55
  5. Geometric realization

    • Izak Moerdijk
    Pages 57-76
  6. Comparison theorems

    • Izak Moerdijk
    Pages 77-88
  7. Back Matter

    Pages 89-94

About this book

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

  • Book Title: Classifying Spaces and Classifying Topoi

  • Authors: Izak Moerdijk

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0094441

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • eBook ISBN: 978-3-540-44912-6Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 98

  • Topics: K-Theory, Algebraic Topology

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions