Third in a three part set, this volume introduces topos theory and the idea of sheaves.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
" . . . these volumes will be of enormous value to graduate students in pure or applied category theory." Martin Hyland, Mathematical Reviews
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.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 cour. Codice articolo 446935689
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Hardcover. Condizione: new. Hardcover. 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 last five chapters are then devoted to an axiomatic approach to the categories of sheaves, via the theory of elementary toposes. First are established the exactness properties of toposes. A long chapter is devoted to a careful, accessible and extensive description of the internal logic of toposes, a very powerful tool. The book ends by looking at three specific topics: the natural number object in a topos, the Boolean toposes and the theory of sheaves in an arbitrary topos. This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. Notions of sketchability and accessible categories are discussed, and an axiomatic generalization of the category of sheaves is given. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9780521441803
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Hardcover. Condizione: new. Hardcover. 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 last five chapters are then devoted to an axiomatic approach to the categories of sheaves, via the theory of elementary toposes. First are established the exactness properties of toposes. A long chapter is devoted to a careful, accessible and extensive description of the internal logic of toposes, a very powerful tool. The book ends by looking at three specific topics: the natural number object in a topos, the Boolean toposes and the theory of sheaves in an arbitrary topos. This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. Notions of sketchability and accessible categories are discussed, and an axiomatic generalization of the category of sheaves is given. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Codice articolo 9780521441803
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