Handbook of Categorical Algebra: Volume 3, Sheaf Theory
Author | : Francis Borceux |
Publisher | : Cambridge University Press |
Total Pages | : 544 |
Release | : 1994-12-08 |
ISBN-10 | : 9780521441803 |
ISBN-13 | : 0521441803 |
Rating | : 4/5 (803 Downloads) |
Download or read book Handbook of Categorical Algebra: Volume 3, Sheaf Theory written by Francis Borceux and published by Cambridge University Press. This book was released on 1994-12-08 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.