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Classifying Spaces and Classifying Topoi

  • Book
  • © 1995

Overview

Authors:
  1. Izak Moerdijk
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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
    Download chapter PDF

  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. Erratum to: Classifying spaces and classifying topoi

    • Izak Moerdijk
    Pages 95-95

  8. Back Matter

    Pages 89-94
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Keywords

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.

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

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