Handbook of Categorical Algebra: Volume 3, Sheaf Theory

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Cambridge University Press, 8 déc. 1994 - 522 pages
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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.
 

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Table des matières

1 Locales
1
2 Sheaves
87
3 Grothendieck toposes
192
4 The classifying topos
244
5 Elementary toposes
288
6 Internal logic of a topos
342
7 The law of excluded middle
432
8 The axiom of infinity
453
9 Sheaves in a topos
486
Bibliography
514
Index
517
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