Section Section Description Page Number
1 Introduction p. 1
1.1 A brief history of category theory p. 4
1.2 Intention of this book p. 5
1.3 What is requested from the student p. 7
1.4 Category theory references p. 7
2 The Category of Sets p. 9
2.1 Sets and functions p. 9
2.2 Commutative diagrams p. 23
2.3 Ologs p. 24
3 Fundamental Considerations in Set p. 41
3.1 Products and coproducts p. 41
3.2 Finite limits in Set p. 55
3.3 Finite colimits in Set p. 75
3.4 Other notions in Set p. 90
4 Categories and Functors, Without Admitting It p. 115
4.1 Monoids p. 116
4.2 Groups p. 140
4.3 Graphs p. 146
4.4 Orders p. 162
4.5 Databases: schemas and instances p. 184
5 Basic Category Theory p. 203
5.1 Categories and functors p. 203
5.2 Common categories and functors from pure math p. 239
5.3 Natural transformations p. 267
5.4 Categories and schemas are equivalent, Cat [$$$] Sch p. 306
6 Fundamental Considerations of Categories p. 315
6.1 Limits and colimits p. 315
6.2 Other notions in Cat p. 360
7 Categories at Work p. 375
7.1 Adjoint functors p. 375
7.2 Categories of functors p. 401
7.3 Monads p. 433
7.4 Operads p. 452
References p. 475
Index p. 479
