Tool and Object A History and Philosophy of Category Theory
The book is first of all a history of category theory from the beginnings to A. Grothendieck and F.W. Lawvere. Category theory was an important conceptual tool in 20th century mathematics whose influence on some mathematical subdisciplines (above all alge
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Edited by Eberhard Knobloch and Erhard Scholz Editorial Board: K. Andersen, Aarhus D. Buchwald, Pasadena H.J.M. Bos, Utrecht U. Bottazzini, Roma J.Z. Buchwald, Cambridge, Mass. K. Chemla, Paris S.S. Demidov, Moskva E.A. Fellmann, Basel M. Folkerts, München P. Galison, Cambridge, Mass. I. Grattan-Guinness, London J. Gray, Milton Keynes
R. Halleux, Liège S. Hildebrandt, Bonn Ch. Meinel, Regensburg J. Peiffer, Paris W. Purkert, Leipzig D. Rowe, Mainz A.I. Sabra, Cambridge, Mass. Ch. Sasaki, Tokyo R.H. Stuewer, Minneapolis H. Wußing, Leipzig V.P. Vizgin, Moskva
Ralf Krömer
Tool and Object A History and Philosophy of Category Theory
Birkhäuser Basel · Boston · Berlin
Author Ralf Krömer Goran Peskir School of Mathematics LPHS-Archives Poincaré The University (UMR7117 CNRS) of Manchester Sackville Street Université Nancy 2 Manchester Campus Lettres M60Bd 23, 1QD Albert 1er UnitedNancy 54015 Kingdom Cedex e-mail: [email protected] France e-mail: [email protected]
AMS MSC 2000 Code: 18-03
Library of Congress Control Number: 2007920230 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbiographie; detailed bibliographic data is available in the internet at http://dnb.ddb.de
ISBN: 978-3-7643-7523-2 Birkhäuser Verlag AG, Basel – Boston – Berlin 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 other ways, and storage in data banks. For any kind of use, permission of the copyright owner must be obtained.
© 2007 Birkhäuser Verlag AG, P.O.Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp Cover illustration: left: Saunders Mac Lane, right: Samuel Eilenberg Printed in Germany ISBN-10: 3-7643-7523-X ISBN-13: 978-3-7643-7523-2
987654321
e-ISBN-10: 3-7643-7524-8 e-ISBN-13: 978-3-7643-7524-9
For A.
Acknowledgements First of all, I am indebted to Ernst-Ulrich Gekeler and Gerhard Heinzmann who supervised extensively the research exposed in the present work. It was written chiefly at the Archives Poincaré at Nancy/France, and I wish to thank the staff of this extraordinary research institution for an incomparable atmosphere. When I defended the original German version of the book as my doctoral thesis, Pierre Cartier, Denis Miéville, Philippe Nabonnand, Norbert Schappacher, Rainer Schultze-Pillot and Klaus Volkert participated in the jury, and I thank them for many hints and suggestions. Further thanks for extensive discussions go to Steve Awodey, Liliane Beaulieu, Guillaume Bonfante, Jessica Carter, Bruno Fabre, Dominique Fagnot, Anders Kock, F. William Lawvere, Philippe Lombard, Jean-Pierre Marquis and Colin McLarty. Valuable hints have further been provided by Pierre Ageron, Patrick Blackburn, Jean Bénabou, Leo Corry, Jacques Dixmier, Marie-Jo Durand-R
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