Cargando…
Handbook of categorical algebra 3 : categories of sheaves /
The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned also to serve as a reference book for both specialist...
| 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 ;
volume 53. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half-title; Title; Copyright; Dedication; Contents; Preface to volume; Introduction to this handbook; 1 Locales; 1.1 The intuitionistic propositional calculus; 1.2 Heyting algebras; 1.3 Locales; 1.4 Limits and colimits of locales; 1.5 Nuclei; 1.6 Open morphisms of locales; 1.7 Etale morphisms of locales; 1.8 The points of a locale; 1.9 Sober spaces; 1.10 Compactness conditions; 1.11 Regularity conditions; 1.12 Exercises; 2 Sheaves; 2.1 Sheaves on a locale; 2.2 Closed subobjects; 2.3 Some categorical properties of sheaves; 2.4 Etale spaces; 2.5 The stalks of a topological sheaf
- 4.2 The classifying topos of a finite limit theory4.3 The classifying topos of a geometric sketch; 4.4 The classifying topos of a coherent theory; 4.5 Diaconescu's theorem; 4.6 Exercises; 5 Elementary toposes; 5.1 The notion of a topos; 5.2 Examples of toposes; 5.3 Monomorphisms in a topos; 5.4 Some set theoretical notions in a topos; 5.5 Partial morphisms; 5.6 Injective objects; 5.7 Finite colimits; 5.8 The slice toposes; 5.9 Exactness properties of toposes; 5.10 Union of subobjects; 5.11 Morphisms of toposes; 5.12 Exercises; 6 Internal logic of a topos; 6.1 The language of a topos
- 8 The axiom of infinity8.1 The natural number object; 8.2 Infinite objects in a topos; 8.3 Arithmetic in a topos; 8.4 The trichotomy; 8.5 Finite objects in a topos; 8.6 Exercises; 9 Sheaves in a topos; 9.1 Topologies in a topos; 9.2 Sheaves for a topology; 9.3 The localizations of a topos; 9.4 The double negation sheaves; 9.5 Exercises; Bibliography; Index