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  1. Home
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  3. Handbook of Categorical Algebra
  • Cited by 104
  • Volume 3: Sheaf Theory
  • Francis Borceux, Université Catholique de Louvain, Belgium
Publisher:
Cambridge University Press
Online publication date:
February 2010
Print publication year:
1994
Online ISBN:
9780511525872
DOI:
https://doi.org/10.1017/CBO9780511525872
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets
Series:
Encyclopedia of Mathematics and its Applications (52)
Information

Book 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.

Reviews

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

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