Contents Preface xvii Part 1. The Language of Categories Chapter 1. Categories and Functors 3 §1.1. Diagrams 3 §1.2. Categories 5 §1.3. Functors 7 §1.4. Natural Transformations 11 §1.5. Duality 14 §1.6. Products and Sums 15 §1.7. Initial and Terminal Objects 18 §1.8. Group and Cogroup Objects 21 §1.9. Homomorphisms 24 §1.10. Abelian Groups and Cogroups 25 §1.11. Adjoint Functors 26 Chapter 2. Limits and Colimits 29 §2.1. Diagrams and Their Shapes 29 §2.2. Limits and Colimits 31 §2.3. Naturality of Limits and Colimits 34 §2.4. Special Kinds of Limits and Colimits 35 §2.5. Formal Properties of Pushout and Pullback Squares 40 vii
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