Handbook of Categorical Algebra: Volume 3, Sheaf Theory

TRAMA

Third in a three part set, this volume introduces topos theory and the idea of sheaves.

NOTE EDITORE

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.

SOMMARIO

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.

PREFAZIONE

The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. There is ample material here for a graduate course in category theory, and the books should also serve as a reference for users.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780521061247
• Collana: Encyclopedia of Mathematics and its Applications
• Dimensioni: 234 x 27 x 155 mm Ø 764 gr
• Formato: Brossura
• Illustration Notes: 162 b/w illus. 94 exercises
• Pagine Arabe: 544