Category Theory has, in recent years, become increasingly important and popular in computer science, and many universities now introduce Category Theory as part of the curriculum for undergraduate computer science students. Here, the theory is developed in a straightforward way, and is enriched with many examples from computer science.
Author(s): R.F.C. Walters
Series: Cambridge Computer Science Texts 28
Publisher: Cambridge University Press
Year: 1992
Language: English
Commentary: Front and back covers, OCR, 2 level bookmarks, paginated.
Pages: 180
Front Cover......Page 1
Preface......Page 9
Contents......Page 11
Introduction......Page 13
1. Categories......Page 15
2. General Examples......Page 20
3. Free Categories Generators and Relations......Page 22
4. Some Large Categories......Page 26
5. The Dual of a Category......Page 28
Problems......Page 32
1. Initial and Terminal objects......Page 37
2. Products......Page 39
3. Categories with Products Circuits......Page 44
4. Products of Families......Page 51
5. Sums......Page 54
6. Categories with Sums Flow Charts......Page 57
Problems......Page 64
1. The Distributive Law......Page 67
2. Examples......Page 70
3. Imperative Programs......Page 74
Problems......Page 80
1. Arithmetic......Page 83
2. Stacks......Page 86
3. Arrays......Page 92
4. Binary Trees......Page 93
5. Queues......Page 95
6. Pointers......Page 98
7. Turing Machines......Page 99
Problems......Page 102
1. Functors......Page 105
2. Functor Categories......Page 111
3. Directed Graphs and Regular Grammars......Page 114
4. Automata and Imperative Programs with Input......Page 124
5. The Specification of Functions......Page 128
6. What Does Free Mean......Page 132
7. Adjoint Functors......Page 135
Problems......Page 138
1. The Free Category with Products......Page 141
2. Functional Specification with Products......Page 145
3. Context-free Languages......Page 149
4. Natural Numbers and Cartesian Closed Categories......Page 150
Problems......Page 153
1. The Knuth-Bendix Procedure......Page 155
2. Computing Left Kan Extensions......Page 159
Problems......Page 171
References......Page 173
Index......Page 175
Back Cover......Page 180
