Handbook of Categorical Algebra: Volume 3, Sheaf Theory

Third in a three part set, this volume introduces topos theory and the idea of sheaves.

Francis Borceux (Author)

9780521441803, Cambridge University Press

Hardback, published 8 December 1994

544 pages, 162 b/w illus. 94 exercises
24.1 x 16.1 x 3.3 cm, 0.929 kg

" . . . these volumes will be of enormous value to graduate students in pure or applied category theory." Martin Hyland, Mathematical Reviews

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.

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.

Subject Areas: Mathematical foundations [PBC]