Category Theory Proceedings of the International Conference held in
With one exception, these papers are original and fully refereed research articles on various applications of Category Theory to Algebraic Topology, Logic and Computer Science. The exception is an outstanding and lengthy survey paper by Joyal/Street (80 p
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Lecture Notes in Mathematics Editors: A. Dold, Heidelberg B. Eckmann, Zurich F. Takens, Groningen
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A. Carboni
M. C. Pedicchio
G. Rosolini
Category Theory Proceedings of the International Conference held in Como, Italy, July 22-28, 1990
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
(Eds.)
Editors Aurelio Carboni Dipartimento di Matematica Universita di Milano Via C. Saldini 50 20133 Milano, Italy Maria Cristina Pedicchio Dipartimento di Scienze Matematiche Universita di Trieste Piazzale Europa 1 34100 Trieste, Italy Guiseppe Rosolini Dipartimento di Matematica Universita di Parma 43100 Parma, Italy
Mathematics Subject Classification (1991): 18-06
ISBN 3-540-54706-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-54706-1 Springer-Verlag New York Berlin Heidelberg 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 1991 Printed in Germany Typesetting: Camera ready by author Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 46/3140-543210 - Printed on acid-free paper
v PREFACE
The Conference "Category Theory '90" was held in Como (Italy) from July 22 to July 28, 1990. The organizing committee was composed of: A. Carboni, University of Milan, Italy M.C. Pedicchio, University of Trieste, Italy G. Rosolini, University of Parma, Italy. The scientific committee was composed of: J. Adamek (Prague), J. Benabou (Paris), A. Heller (New York), P.T. Johnstone (Cambridge), G.M. Kelly (Sydney), F. W. Lawvere (Buffalo). 125 persons took part to the Conference and 46 of them gave a talk. The editors would like to express their gratitude to the organisms that supported the meeting: "Consiglio Nazionale delle Ricerche" "Gruppi Nazionali ./.0% di Topologia e Loqica" Universities of Milan, Parma and Trieste, as well as to all referees for their competent and prompt collaboration and to Springer for publishing the Proceedings. The volume is divided in two parts: the first one contains research papers and is preceded by an introductory article by F.W. Lawvere; the second part consists of a monograph by A. Joyal and R. Street on Tannaka duality and quantum groups. It is intended to be an introduction to this rapidly growing subject and is addressed to a wider audience than category theorists; the paper is not only expository, but also contains new results and new proofs of classical results.
TABLE OF CONTENTS
PART I F.W. LAWVERE, Some thoughts on the future of category theory
p.
J. A
