文档介绍：Contents
Preface iii
1 Finite discrete sketches 1
Sketches with sums 1
The sketch for ¯elds 3
Term algebras for FD sketches 5
2 More about sketches 12
Finite limit sketches 12
Initial term models of FL sketches 16
The theory of an FL sketch 19
General de¯nition of sketch 21
3 The category of sketches 26
Homomorphisms of sketches 26
Parametrized data types as pushouts 28
The model category functor 33
4 Fibrations 38
Fibrations 38
The Grothendieck construction 43
An equivalence of categories 48
Wreath products 51
5 Toposes 56
De¯nition of topos 57
Properties of toposes 60
Is a two-element plete? 64
Presheaves 66
Sheaves 67
Fuzzy sets 72
External functors 75
The realizability topos 79
i
ii Contents
Answers to Exercises 83
Solutions for Chapter 1 83
Solutions for Chapter 2 85
Solutions for Chapter 3 87
Solutions for Chapter 4 88
Solutions for Chapter 5 92
Bibliography 97
Index 102
Preface
This is the electronic supplement to Category Theory puting Sci-
ence, second edition, Prentice-Hall International, 1995, ISBN 0-13-
323809-1. It consists of (revisions of) ¯ve chapters from the ¯rst edition of that
book, as well as continuing updates of the ¯rst and second editions.
The chapters included here are, as numbered in the ¯rst edition, Chapters 7
(Finite discrete sketches), 9 (More about sketches), 10 (The category of sketches),
11 (Fibrations) and 14 (Toposes).
References, both in the published book and here to material in this electronic
supplement are pre¯xed by ` ES', while references to the printed book are un-
adorned. Thus a reference to of Chapter 3 is a reference to Section of
Chapter 3 of the printed book, while references to Section of Chapter ES 3 is
a reference to Section of Chapter 3 of this supplement. A reference without a
chapter number refers, as usual, to the current chapt