Singular Coverings of Toposes
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
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Marta Bunge Jonathon Funk
Singular Coverings of Toposes
1890
Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1890
M. Bunge · J. Funk
Singular Coverings of Toposes
ABC
Authors Jonathon Funk (Lecturer) Department of Computer Science, Mathematics, and Physics The University of the West Indies Cave Hill Campus P.O. Box 64, Bridgetown BB11000, Barbados e-mail: [email protected]
Marta Bunge (Professor Emerita) Department of Mathematics McGill University 805 Sherbrooke Street West Montréal, Québec, H3A 2K6 Canada e-mail: [email protected]
Library of Congress Control Number: 2006928617 Mathematics Subject Classification (2000): Primary: 18B25, 57M 12; Secondary: 18C15, 06E15 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-36359-9 Springer Berlin Heidelberg New York ISBN-13 978-3-540-36359-0 Springer Berlin Heidelberg New York DOI 10.1007/3-540-36359-9
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543210
Dedicated to F. W. Lawvere
Preface
This book gives an introduction to a theory of complete spreads, which basically uses the same strategy employed by R.H. Fox [Fox57] for dealing with branched coverings, and which we carry out in close connection with (and parallel to) a theory of distributions in the sense of F. W. Lawvere [Law66, Law83, Law92]. Rather than elucidating the concepts of toposes, distributions, and complete spreads in this preface, we give a preliminary taste of these concepts by including certain quotations which authoritatively describe the original settings and motivations behind them, and let the reader explore these concepts and their interplay in the often new guises in which we present them in this book, itself based on our own work on these topics during the past ten years.
Toposes “The original notion of a topos, as a ‘generalized space’ suitable for supporting the exotic cohomology theories required in algebraic g
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