Classifying Spaces and Classifying Topoi
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 construc
- PDF / 6,641,162 Bytes
- 100 Pages / 432 x 666 pts Page_size
- 0 Downloads / 239 Views
1616
Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo
1. Moerdijk
Classifying Spaces and Classifying Topoi
Springer
Author Izak Moerdijk Mathematisch Institut Universiteit Utrecht P.O. Box 80.010 3508 TA Utrecht, The Netherlands
Cataloging-in-Publication Data applied for
Die Deutsche Bibliothek - CIP-Einheitsaufnahme Moerdijk, Izak: Classifying spaces and classifying topoi / Izak Moerdijk. Berlin; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Tokyo: Springer, 1995 (Lecture notes in mathematics ; 1616) ISBN 3-540-60319-0 NE:GT
Mathematics Subject Classification (1991): 18FI0, 55N30, 55P15 ISBN 3-540-60319-0 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1995 Printed in Germany Typesetting: Camera-ready TEX output by the author 46/3142-543210 - Printed on acid-free paper SPIN: 10479497
Preface In these notes, a detailed account is presented of the relation between classifying spaces and classifying topoi. To make the notes more accessible, I have tried to keep the prerequisites to a minimum, for example by starting with an introductory chapter on topos theory, and by reviewing the necessary basic properties of geometric realization and classifying spaces in the first part of Chapter III. Furthermore, I have made an attempt to present the material in such a way that it is possible to read the special case of discrete categories first. This case already provides a good general picture, while it avoids some of the technical complications involved in the general case of topological categories. Thus, to reach the comparison and classification theorems for discrete categories in Section IV.1, the reader can omit §§3,4,5,7 and most of §6 in Chapter II, as well as the second parts of §1 and §2 in Chapter III. In the past several years I have been helped by discussions with several people which were directly or indirectly related to the subject matter of these notes. In this respect, I am particularly indebted to W.T. van Est, S. Mac Lane, G. Segal and J.A. Svensson. Above all, A. Joyal taught me not to underestimate the Sierpinski space. A summary of the main results appeared in the Comptes Rendus de I' Academic des Sciences (t. 317, 1993). The present version was mainly written during the fall of 1994, which I spent at the University of Aarhus. I am most grateful for the hospitality and support of the mat
Data Loading...
