| Preface to the Second Edition Preface to the First Edition Introduction I. Categories, Functors, and Natural Transformations 1. Axioms for Categories 2. Categories 3. Functors 4. Natural Transformations 5. Monics, Epis, and Zeros 6. Foundations 7. Large Categories 8. Hom-Sets II. Constructions on Categories 1. Duality 2. Contravariance and Opposites 3. Products of Categories 4. Functor Categories 5. The Category of All Categories 6. Comma Categories 7. Graphs and Free Categories 8. Quotient Categories III. Universals and Limits 1. Universal Arrows 2. The Yoneda Lemma 3. Coproducts and Colimits 4. Products and Limits 5. Categories with Finite Products 6. Groups in Categories 7. Colimits of Representable Functors IV. Adjoints 1. Adjunctions 2. Examples of Adjoints 3. Reflective Subcategories 4. Equivalence of Categories 5. Adjoints for Preorders 6. Cartesian Closed Categories 7. Transformations of Adjoints 8. Composition of Adjoints 9. Subsets and Characteristic Functions 10. Categories Like Sets V. Limits 1. Creation of Limits 2. Limits by Products and Equalizers 3. Limits with Parameters 4. Preservation of Limits 5. Adjoints on Limits 6. Freyd's Adjoint Functor Theorem 7. Subobjects and Generators 8. The Special Adjoint Functor Theorem 9. Adjoints in Topology VI. Monads and Algebras 1. Monads in a Category 2. Algebras for a Monad 3. The Comparison with Algebras 4. Words and Free Semigroups 5. Free Algebras for a Monad 6. Split Coequalizers 7. Beck's Theorem 8. Algebras Are T-Algebras 9. Compact Hausdorff Spaces VII. Monoids 1. Monoidal Categories 2. Coherence 3. Monoids 4. Actions 5. The Simplicial Category 6. Monads and Homology 7. Closed Categories 8. Compactly Generated Spaces 9. Loops and Suspensions VIII. Abelian Categories IX. Special Limits X. Kan Extensions XI. Symmetry and Braiding in Monoidal Categories XII. Structures in Categories Appendix. Foundations Table of Standard Categories: Objects and Arrows Table of Terminology Bibliography Index |
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