文档介绍：Foundations puting S~
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This Page Intentionally No Longer Blank
Basic Category Theory
puter Scientists
Benjamin C. Pierce
The MIT Press
Cambridge, Massachusetts
London, England
C 1991 Massachusetts Institute of Technology
All right reserved. No part of this book may be reproduced in any form by any
electronic or mechanical means (including photocopying, recording, or information
storage and retrieval) without permission in writing from the publisher.
This book was typeset by the author using and converted to PostScript
using Y&:Y's M. Camera-ready copy was produced by Chiron, Inc.
Printed and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Pierce, Benjamin C.
Basic category theory puter scientists I Benjamin C. Pierce.
p. em.- (Foundations puting)
Includes bibliographical references and index.
ISBN 0-262-66071-7
1. Computer science-Mathematics. 2. Categories (Mathematics) I. Title. ll. Series.
1991
-dc20 91-8489
CIP
10 9 8 7
To Roger, Alexandra, and Jessica
Contents
Series Foreword ix
Preface xi
1 Basic Constructions 1
Categories 1
Diagrams 10
Monomorphisms, Epimorphisms, and Isomorphisms 13
Initial and Terminal Objects 16
Products 17
Universal Constructions 20
Equalizers 21
Pullbacks 22
Limits 26
Exponentiation 33
2 Functors, Natural Transformations, and Adjoints 36
Functors 36
F-Algebras 39
Natural Transformations 41
Adjoints 45
3 Applications 53
Cartesian Closed Categories 53
Implicit Conversions and Generic Operators 57
Programming Language Semantics 59
Recursive Domain Equations 61
4 Further Reading 73
Textbooks 73
Introductory Articles 74
Reference Books 76
Selected Research Articles 78
Bibliography 81
Summary of Notation 93