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 Front Cover.djvu
Contents ......Page 0004.djvu
Introduction ......Page 0010.djvu
Exercises on Extremal Categories ......Page 0020.djvu
Exercises on Typical Categories ......Page 0021.djvu
CHAPTER 1. FUNDAMENTALS ......Page 0023.djvu
1.1. Contravariant Functors and Dual Categories ......Page 0024.djvu
1.3. The Standard Functors ......Page 0025.djvu
1.4. Special Maps ......Page 0026.djvu
1.5. Subobjects and Quotient Objects ......Page 0028.djvu
1.6. Difference Kernels and Cokernels ......Page 0030.djvu
1.7. Products and Sums ......Page 0031.djvu
1.8. Complete Categories ......Page 0034.djvu
1.9. Zero Objects, Kernels, and Cokernels ......Page 0035.djvu
Exercises ......Page 0036.djvu
CHAPTER 2. FUNDAMENTALS OF ABELIAN CATEGORIES ......Page 0044.djvu
2.1. Theorems for Abelian Categories ......Page 0045.djvu
2.2. Exact Sequences ......Page 0053.djvu
2.3. The Additive Structure for Abelian Categories ......Page 0054.djvu
2.4. Recognition of Direct Sum Systems ......Page 0059.djvu
2.5. The Pullback and Pushout Theorems ......Page 0060.djvu
2.6. Classical Lemmas ......Page 0063.djvu
Exercises ......Page 0069.djvu
3.1. Additivity and Exactness ......Page 0073.djvu
3.2. Embeddings ......Page 0075.djvu
3.3. Special Objects ......Page 0076.djvu
3.4. Subcategories ......Page 0079.djvu
3.6. Bifunctors ......Page 0081.djvu
Exercises ......Page 0083.djvu
CHAPTER 4. METATHEOREMS ......Page 0103.djvu
4.1. Very Abelian Categories ......Page 0104.djvu
4.2. First Metatheorem ......Page 0105.djvu
4.3. Fully Abelian Categories ......Page 0106.djvu
4.4. Mitchell's Theorem ......Page 0109.djvu
Exercises ......Page 0112.djvu
5.1. Abelianness ......Page 0118.djvu
5.2. Grothendieck Categories ......Page 0120.djvu
5.3. The Representation Functor ......Page 0121.djvu
Exercises ......Page 0124.djvu
6.1. Extensions ......Page 0132.djvu
6.2. Envelopes ......Page 0135.djvu
Exercises ......Page 0140.djvu
7.1. First Embedding ......Page 0147.djvu
7.2. An Abstraction ......Page 0150.djvu
7.3. The Abelianness of the Categories of Absolutely Pure Objects and Left-Exact Functors ......Page 0157.djvu
Exercises ......Page 0159.djvu
APPENDIX ......Page 0164.djvu
BIBLIOGRAPHY ......Page 0170.djvu
INDEX ......Page 0172.djvu
Back Cover ......Page Back Cover.djvu
