Contents

1 Introduction

1.1 A brief history of category theory

1.2 Intention of this book

1.3 What is requested from the student

1.4 Category theory references

2 The Category of Sets

2.1 Sets and functions

2.2 Commutative diagrams

2.3 Ologs

3 Fundamental Considerations in Set

3.1 Products and coproducts

3.2 Finite limits in Set

3.3 Finite colimits in Set

3.4 Other notions in Set

4 Categories and Functors, Without Admitting It

4.1 Monoids

4.2 Groups

4.3 Graphs

4.4 Orders

4.5 Databases: schemas and instances

5 Basic Category Theory

5.1 Categories and functors

5.2 Common categories and functors from pure math

5.3 Natural transformations

5.4 Categories and schemas are equivalent, Cat » Sch

6 Fundamental Considerations of Categories

6.1 Limits and colimits

6.2 Other notions in Cat

7 Categories at Work

7.1 Adjoint functors

7.2 Categories of functors

7.3 Monads

7.4 Operads

References

Index