Handbook of Categorical Algebra

Volume 3, Sheaf Theory
Erscheinungsjahr 2008
ISBN: 978-0-521-06124-7
Verlag: Cambridge University Press

Buch, Englisch, Band 52, 544 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 816 g

Reihe: Encyclopedia of Mathematics and its Applications

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.

Autoren/Hrsg.

Borceux, Francis

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Elementare Algebra

Inhaltsverzeichnis

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.