Handbook of Categorical Algebra: Volume 3, Sheaf Theory
Seiten
2008
Cambridge University Press (Verlag)
978-0-521-06124-7 (ISBN)
Cambridge University Press (Verlag)
978-0-521-06124-7 (ISBN)
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.
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.
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.
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.
| Erscheint lt. Verlag | 24.4.2008 |
|---|---|
| Reihe/Serie | Encyclopedia of Mathematics and its Applications |
| Zusatzinfo | Worked examples or Exercises; 162 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 155 x 234 mm |
| Gewicht | 764 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-521-06124-5 / 0521061245 |
| ISBN-13 | 978-0-521-06124-7 / 9780521061247 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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