Handbook of Categorical Algebra: Volume 3, Sheaf Theory
Series: Encyclopedia of Mathematics and its Applications; 52;
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Product details:
- Edition number and title Sheaf Theory v. 3
- Publisher Cambridge University Press
- Date of Publication 8 December 1994
- ISBN 9780521441803
- Binding Hardback
- No. of pages544 pages
- Size 241x161x33 mm
- Weight 929 g
- Language English
- Illustrations 162 b/w illus. 94 exercises 0
Categories
Short description:
Third in a three part set, this volume introduces topos theory and the idea of sheaves.
MoreLong description:
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.
" . . . these volumes will be of enormous value to graduate students in pure or applied category theory." Martin Hyland, Mathematical Reviews
Table of Contents:
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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