Categories of sheaves
著者
書誌事項
Categories of sheaves
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 53 [i.e. 52] . Handbook of categorical algebra ; 3）
Cambridge University Press, 1994
- : hbk
- pbk
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注記
Bibliography: p. 514-516
Includes index
内容説明・目次
内容説明
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 specialists in the field and all those using category theory as a tool. Volume 3 begins with the essential aspects of the theory of locales, proceeding to a study in chapter 2 of the sheaves on a locale and on a topological space, in their various equivalent presentations: functors, etale maps or W-sets. Next, this situation is generalized to the case of sheaves on a site and the corresponding notion of Grothendieck topos is introduced. Chapter 4 relates the theory of Grothendieck toposes with that of accessible categories and sketches, by proving the existence of a classifying topos for all coherent theories.
目次
- Preface
- Introduction to the handbook
- 1. Locales
- 2. Sheaves
- 3. Grothendieck toposes
- 4. The classifying topos
- 5. Elementary toposes
- 6. Internal logic of a topos
- 7. The law of excluded middle
- 8. The axiom of infinity
- 9. Sheaves in a topos
- Index.
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