Abelian Categories: An Introduction to the Theory of...

Abelian Categories: An Introduction to the Theory of Functors

Peter Freyd
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CONTENTS
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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
CHAPTER 7. EMBEDDING THEOREMS
7.1. First Embedding
7.2. An Abstraction
7.3. The Abelianness of the Categories of Absolutely Pure Objects and Left-Exact Functors
Exercises
APPENDIX
BIBLIOGRAPHY
INDEX
الفئات:
عام:
1964
الإصدار:
1
الناشر:
Harper & Row
اللغة:
english
الصفحات:
176
سلسلة الكتب:
Harper's Series in Modern Mathematics
ملف:
PDF, 2.68 MB
IPFS:
CID , CID Blake2b
english, 1964
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