دانلود کتاب Abelian Categories: An Introduction to the Theory of Functors

CONTENTS========ContentsIntroductionExercises on Extremal CategoriesExercises on Typical CategoriesCHAPTER 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 ExercisesCHAPTER 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 ExercisesCHAPTER 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 ExercisesCHAPTER 4. METATHEOREMS 4.1. Very Abelian Categories 4.2. First Metatheorem 4.3. Fully Abelian Categories 4.4. Mitchell's Theorem ExercisesCHAPTER 5. FUNCTOR CATEGORIES 5.1. Abelianness 5.2. Grothendieck Categories 5.3. The Representation Functor ExercisesCHAPTER 6. INJECTIVE ENVELOPES 6.1. Extensions 6.2. Envelopes ExercisesCHAPTER 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 FunctorsExercisesAPPENDIXBIBLIOGRAPHYINDEX