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
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
Author(s): Peter Freyd
Series: Harper's Series in Modern Mathematics
Edition: 1
Publisher: Harper & Row
Year: 1964
Language: English
Commentary: Covers, 2 level bookmarks, OCR, paginated.
Pages: 176
Front Cover ......Page 1
Contents ......Page 5
Introduction ......Page 11
Exercises on Extremal Categories ......Page 21
Exercises on Typical Categories ......Page 22
CHAPTER 1. FUNDAMENTALS ......Page 24
1.1. Contravariant Functors and Dual Categories ......Page 25
1.3. The Standard Functors ......Page 26
1.4. Special Maps ......Page 27
1.5. Subobjects and Quotient Objects ......Page 29
1.6. Difference Kernels and Cokernels ......Page 31
1.7. Products and Sums ......Page 32
1.8. Complete Categories ......Page 35
1.9. Zero Objects, Kernels, and Cokernels ......Page 36
Exercises ......Page 37
CHAPTER 2. FUNDAMENTALS OF ABELIAN CATEGORIES ......Page 45
2.1. Theorems for Abelian Categories ......Page 46
2.2. Exact Sequences ......Page 54
2.3. The Additive Structure for Abelian Categories ......Page 55
2.4. Recognition of Direct Sum Systems ......Page 60
2.5. The Pullback and Pushout Theorems ......Page 61
2.6. Classical Lemmas ......Page 64
Exercises ......Page 70
3.1. Additivity and Exactness ......Page 74
3.2. Embeddings ......Page 76
3.3. Special Objects ......Page 77
3.4. Subcategories ......Page 80
3.6. Bifunctors ......Page 82
Exercises ......Page 84
CHAPTER 4. METATHEOREMS ......Page 104
4.1. Very Abelian Categories ......Page 105
4.2. First Metatheorem ......Page 106
4.3. Fully Abelian Categories ......Page 107
4.4. Mitchell's Theorem ......Page 110
Exercises ......Page 113
5.1. Abelianness ......Page 119
5.2. Grothendieck Categories ......Page 121
5.3. The Representation Functor ......Page 122
Exercises ......Page 125
6.1. Extensions ......Page 133
6.2. Envelopes ......Page 136
Exercises ......Page 141
7.1. First Embedding ......Page 148
7.2. An Abstraction ......Page 151
7.3. The Abelianness of the Categories of Absolutely Pure Objects and Left-Exact Functors ......Page 158
Exercises ......Page 160
APPENDIX ......Page 165
BIBLIOGRAPHY ......Page 171
INDEX ......Page 173
Back Cover ......Page 176
