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CONTENTS ======== Contents Introduction Exercises on Extremal Categories Exercises on Typical Categories CHAPTER 1. FUNDAMENTALS 1.1. Contravariant Functors and Dual Categories 1.2. Notation 1.3. The Standard Functors 1.4. Special Maps 1.5. Subobjects and Quotient Objects 1.6. Difference Kernels and Cokernels 1.7. Products and Sums 1.8. Complete Categories 1.9. Zero Objects, Kernels, and Cokernels Exercises CHAPTER 2. FUNDAMENTALS OF ABELIAN CATEGORIES 2.1. Theorems for Abelian Categories 2.2. Exact Sequences 2.3. The Additive Structure for Abelian Categories 2.4. Recognition of Direct Sum Systems 2.5. The Pullback and Pushout Theorems 2.6. Classical Lemmas Exercises CHAPTER 3. SPECIAL FUNCTORS AND SUBCATEGORIES 3.1. Additivity and Exactness 3.2. Embeddings 3.3. Special Objects 3.4. Subcategories 3.5. Special Contravariant Functors 3.6. Bifunctors Exercises CHAPTER 4. METATHEOREMS 4.1. Very Abelian Categories 4.2. First Metatheorem 4.3. Fully Abelian Categories 4.4. Mitchell's Theorem Exercises CHAPTER 5. FUNCTOR CATEGORIES 5.1. Abelianness 5.2. Grothendieck Categories 5.3. The Representation Functor Exercises CHAPTER 6. INJECTIVE ENVELOPES 6.1. Extensions 6.2. Envelopes Exercises

Who reads Abelian Categories: An Introduction to the Theory of Functors?

Author

Peter Freyd

Publisher

Harper & Row

Published

1964

Language

EN

Category

nonfiction

Subjects

Mathematics, Stem