Categories and Computer Science

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Category theory has, in recent years, become increasingly important and popular in computer science, and many universities now include it as part of their curriculums. This text is geared to students of mathematics as well as undergraduate computer scientists.
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Editorial Reviews

From the Publisher
"Nice, crisp introduction to category theory, motivated by examples and use in computer science. Mathematical sophistication blends nicely with fundamental concepts and examples to make the connections (and usefulness) understandable to good undergraduates." The American Mathematical Monthly

"Within the setting of distributive categories, nicely explained here, one sees data structure abstractions done properly. The example of queues is the most compelling in that all of the structure of distributive categories is used....strongly recommend[ed]. David B. Benson, Computing Reviews

"...probably the clearest introduction to category theory written to date." The Bulletin of Mathematics Books

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Product Details

  • ISBN-13: 9780521419970
  • Publisher: Cambridge University Press
  • Publication date: 12/28/2006
  • Series: Computer Science Texts Series
  • Pages: 180
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.55 (d)

Table of Contents

Introduction 1
1 The Algebra of Functions 3
1 Categories 3
2 General Examples 8
3 Free Categories; Generators and Relations 10
4 Some Large Categories 14
5 The Dual of a Category 16
Problems 20
2 Products and Sums 25
1 Initial and Terminal objects 25
2 Products 27
3 Categories with Products; Circuits 32
4 Products of Families 39
5 Sums 42
6 Categories with Sums; Flow Charts 45
Problems 52
3 Distributive Categories 55
1 The Distributive Law 55
2 Examples 58
3 Imperative Programs 62
Problems 68
4 Data Types 71
1 Arithmetic 71
2 Stacks 74
3 Arrays 80
4 Binary Trees 81
5 Queues 83
6 Pointers 86
7 Turing Machines 87
Problems 90
5 Categories of Functors 93
1 Functors 93
2 Functor Categories 99
3 Directed Graphs and Regular Grammars 102
4 Automata and Imperative Programs with Input 112
5 The Specification of Functions 116
6 What Does Free Mean? 120
7 Adjoint Functors 123
Problems 126
6 More About Products 129
1 The Free Category with Products 129
2 Functional Specification with Products 133
3 Context-free Languages 137
4 Natural Numbers and Cartesian Closed Categories 138
Problems 141
7 Computational Category Theory 143
1 The Knuth-Bendix Procedure 143
2 Computing Left Kan Extensions 147
Problems 159
References 161
Index 163
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