Handbook of categorical algebra. 3, Categories of sheaves /
Francis Borceux.
- Cambridge : Cambridge University Press, 1994.
- 1 online resource (xvii, 522 pages) : digital, PDF file(s).
- Encyclopedia of mathematics and its applications ; volume 52 .
- Encyclopedia of mathematics and its applications ; v. 52. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.