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Handbook of categorical algebra 2 : categories and structures /
The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the materia...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
[1994]
|
| Colección: | Encyclopedia of mathematics and its applications ;
51. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title; Title; Copyright; Dedication; Contents; Preface to volume 2; Introduction to this handbook; 1 Abelian categories; 1.1 Zero objects and kernels; 1.2 Additive categories and biproducts; 1.3 Additive functors; 1.4 Abelian categories; 1.5 Exactness properties of abelian categories; 1.6 Additivity of abelian categories; 1.7 Union of subobjects; 1.8 Exact sequences; 1.9 Diagram chasing; 1.10 Some diagram lemmas; 1.11 Exact functors; 1.12 Torsion theories; 1.13 Localizations of abelian categories; 1.14 The embedding theorem; 1.15 Exercises; 2 Regular categories
- 2.1 Exactness properties of regular categories2.2 Definition in terms of strong epimorphisms; 2.3 Exact sequences; 2.4 Examples; 2.5 Equivalence relations; 2.6 Exact categories; 2.7 An embedding theorem; 2.8 The calculus of relations; 2.9 Exercises; 3 Algebraic theories; 3.1 The theory of groups revisited; 3.2 A glance at universal algebra; 3.3 A categorical approach to universal algebra; 3.4 Limits and colimits in algebraic categories; 3.5 The exactness properties of algebraic categories; 3.6 The algebraic lattices of subobjects; 3.7 Algebraic functors; 3.8 Freely generated models
- 3.9 Characterization of algebraic categories3.10 Commutative theories; 3.11 Tensor product of theories; 3.12 A glance at Morita theory; 3.13 Exercises; 4 Monads; 4.1 Monads and their algebras; 4.2 Monads and adjunctions; 4.3 Limits and colimits in categories of algebras; 4.4 Characterization of monadic categories; 4.5 The adjoint lifting theorem; 4.6 Monads with rank; 4.7 A glance at descent theory; 4.8 Exercises; 5 Accessible categories; 5.1 Presentable objects in a category; 5.2 Locally presentable categories; 5.3 Accessible categories; 5.4 Raising the degree of accessibility
- 5.5 Functors with rank5.6 Sketches; 5.7 Exercises; 6 Enriched category theory; 6.1 Symmetric monoidal closed categories; 6.2 Enriched categories; 6.3 The enriched Yoneda lemma; 6.4 Change of base; 6.5 Tensors and cotensors; 6.6 Weighted limits; 6.7 Enriched adjunctions; 6.8 Exercises; 7 Topological categories; 7.1 Exponentiable spaces; 7.2 Compactly generated spaces; 7.3 Topological functors; 7.4 Exercises; 8 Fibred categories; 8.1 Fibrations; 8.2 Cartesian functors; 8.3 Fibrations via pseudo-functors; 8.4 Fibred adjunctions; 8.5 Completeness of a fibration; 8.6 Locally small fibrations
- 8.7 Definability8.8 Exercises; Bibliography; Index