Ebook: Categories and Computer Science

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.

CONTENTS
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Preface
Introduction
1 The Algebra of Functions
1. Categories
2. General Examples
3. Free Categories Generators and Relations
4. Some Large Categories
5. The Dual of a Category
Problems
2 Products and Sums
1. Initial and Terminal objects
2. Products
3. Categories with Products Circuits
4. Products of Families
5. Sums
6. Categories with Sums Flow Charts
Problems
3 Distributive Categories
1. The Distributive Law
2. Examples
3. Imperative Programs
Problems
4 Data Types
1. Arithmetic
2. Stacks
3. Arrays
4. Binary Trees
5. Queues
6. Pointers
7. Turing Machines
Problems
5 Categories of Functors
1. Functors
2. Functor Categories
3. Directed Graphs and Regular Grammars
4. Automata and Imperative Programs with Input
5. The Specification of Functions
6. What Does Free Mean?
7. Adjoint Functors
Problems
6 More About Products
1. The Free Category with Products
2. Functional Specification with Products
3. Context-free Languages
4. Natural Numbers and Cartesian Closed Categories
Problems
7 Computational Category Theory
1. The Knuth-Bendix Procedure
2. Computing Left Kan Extensions
Problems
References
Index