| Description |
1 online resource (xvii, 522 pages) : illustrations |
| Series |
Encyclopedia of mathematics and its applications ; volume 53 |
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Encyclopedia of mathematics and its applications ; volume 53.
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| Contents |
Cover; Half-title; Title; Copyright; Dedication; Contents; Preface to volume; Introduction to this handbook; 1 Locales; 1.1 The intuitionistic propositional calculus; 1.2 Heyting algebras; 1.3 Locales; 1.4 Limits and colimits of locales; 1.5 Nuclei; 1.6 Open morphisms of locales; 1.7 Etale morphisms of locales; 1.8 The points of a locale; 1.9 Sober spaces; 1.10 Compactness conditions; 1.11 Regularity conditions; 1.12 Exercises; 2 Sheaves; 2.1 Sheaves on a locale; 2.2 Closed subobjects; 2.3 Some categorical properties of sheaves; 2.4 Etale spaces; 2.5 The stalks of a topological sheaf |
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4.2 The classifying topos of a finite limit theory4.3 The classifying topos of a geometric sketch; 4.4 The classifying topos of a coherent theory; 4.5 Diaconescu's theorem; 4.6 Exercises; 5 Elementary toposes; 5.1 The notion of a topos; 5.2 Examples of toposes; 5.3 Monomorphisms in a topos; 5.4 Some set theoretical notions in a topos; 5.5 Partial morphisms; 5.6 Injective objects; 5.7 Finite colimits; 5.8 The slice toposes; 5.9 Exactness properties of toposes; 5.10 Union of subobjects; 5.11 Morphisms of toposes; 5.12 Exercises; 6 Internal logic of a topos; 6.1 The language of a topos |
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8 The axiom of infinity8.1 The natural number object; 8.2 Infinite objects in a topos; 8.3 Arithmetic in a topos; 8.4 The trichotomy; 8.5 Finite objects in a topos; 8.6 Exercises; 9 Sheaves in a topos; 9.1 Topologies in a topos; 9.2 Sheaves for a topology; 9.3 The localizations of a topos; 9.4 The double negation sheaves; 9.5 Exercises; Bibliography; Index |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 514-516) and index |
| Notes |
Print version record |
| Subject |
Categories (Mathematics)
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Algebra, Homological.
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Abelian categories.
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MATHEMATICS -- Essays.
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MATHEMATICS -- Pre-Calculus.
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MATHEMATICS -- Reference.
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Abelian categories
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Algebra, Homological
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Categories (Mathematics)
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Catégories (Mathématiques)
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Faisceaux, théorie des.
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Topos (Mathématiques)
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| Form |
Electronic book
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| ISBN |
9781107088504 |
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110708850X |
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