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Joseph J. Rotman
An Introduction to
Homological Algebra
Second Edition
123
Joseph J. Rotman
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana IL 61801
USA
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Editorial board:
Sheldon Axler, San Francisco State University
Vincenzo Capasso, Universita` degli Studi di Milano
Carles Casacuberta, Universitat de Barcelona
Angus MacIntyre, Queen Mary, University of London
h Ribet, University of California, Berkeley
Claude Sabbah, CNRS, Ecole´ Polytechnique
Endre Suli,¨ University of Oxford
Wojbor Woyczynski, Case Western Reserve University
ISBN: 978-0-387-24527-0 e-ISBN: 978-0-387-68324-9
DOI -0-387-68324-9
Library of Congress Control Number: 2008936123
Mathematics Subject Classification (2000): 18-01
c Springer Science+Business Media, LLC 2009
All rights reserved. This work may not be translated or copied in whole or in part without the written
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Printed on acid-free paper
To the memory of my mother
Rose Wolf Rotman
Contents
Preface to the Second Edition ................... x
How to Read This Book .......................xiii
Chapter 1 Introduction
Simplicial Homology . ..................... 1
Categories and Functors ..................... 7
Singular Homology . . ...........