Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse.
Assuming a minimal of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic construction and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts.
CONTENTS
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1 Basic Constructions
1.1 Categories
1.2 Diagrams
1.3 Monomorphisms, Epimorphisms, and Isomorphisms
1.4 Initial and Terminal Objects
1.5 Products
1.6 Universal Constructions
1.7 Equalizers
1.8 Pullbacks
1.9 Limits
1.10 Exponentiation
2 Functors, Natural Transformations, and Adjoints
2.1 Functors
2.2 F-Algebras
2.3 Natural Transformations
2.4 Adjoints
3 Applications
3.1 Cartesian Closed Categories
3.2 Implicit Conversions and Generic Operators
3.3 Programming Language Semantics
3.4 Recursive Domain Equations
4 Further Reading
4.1 Textbooks
4.2 Introductory Articles
4.3 Reference Books
4.4 Selected Research Articles
Bibliography
Summary of Notation
Index
Author(s): Benjamin C. Pierce
Series: Foundations of Computing
Edition: 1
Publisher: The MIT Press
Year: 1991
Language: English
Commentary: Front and back covers, OCR, 2 level bookmarks, paginated.
Pages: 114
Front Cover ......Page 1
Title Page ......Page 3
Copyright ......Page 4
Contents ......Page 7
Series Foreword ......Page 8
Preface ......Page 9
1.1 Categories ......Page 13
1.2 Diagrams ......Page 22
1.3 Monomorphisms, Epimorphisms, and Isomorphisms ......Page 25
1.4 Initial and Terminal Objects ......Page 28
1.5 Products ......Page 29
1.6 Universal Constructions ......Page 32
1.7 Equalizers ......Page 33
1.8 Pullbacks ......Page 34
1.9 Limits ......Page 38
1.10 Exponentiation ......Page 45
2.1 Functors ......Page 48
2.2 F-Algebras ......Page 51
2.3 Natural Transformations ......Page 53
2.4 Adjoints ......Page 57
3.1 Cartesian Closed Categories ......Page 65
3.2 Implicit Conversions and Generic Operators ......Page 69
3.3 Programming Language Semantics ......Page 71
3.4 Recursive Domain Equations ......Page 73
4.1 Textbooks ......Page 85
4.2 Introductory Articles ......Page 86
4.3 Reference Books ......Page 88
4.4 Selected Research Articles ......Page 90
Bibliography ......Page 93
Summary of Notation ......Page 105
Index ......Page 107
Back Cover ......Page 114
