Handbook of categorical algebra 3 :: categories of sheaves /
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 specialist...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
[1994]
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
volume 53. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xvii, 522 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 514-516) and index. |
| ISBN: | 9781107088504 110708850X |
Internformat
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| 245 | 1 | 0 | |a Handbook of categorical algebra 3 : |b categories of sheaves / |c Francis Borceux. |
| 246 | 3 | |a Categories of sheaves | |
| 264 | 1 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c [1994] | |
| 264 | 4 | |c ©1994 | |
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v volume 53 | |
| 504 | |a Includes bibliographical references (pages 514-516) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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. | ||
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| 650 | 0 | |a Abelian categories. |0 http://id.loc.gov/authorities/subjects/sh85000127 | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn861692376 |
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| _version_ | 1816882248976171008 |
| adam_text | |
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| author | Borceux, Francis, 1948- |
| author_GND | http://id.loc.gov/authorities/names/n83129031 |
| author_facet | Borceux, Francis, 1948- |
| author_role | |
| author_sort | Borceux, Francis, 1948- |
| author_variant | f b fb |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA169 |
| callnumber-raw | QA169 .B673 1994eb |
| callnumber-search | QA169 .B673 1994eb |
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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 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 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 |
| ctrlnum | (OCoLC)861692376 |
| dewey-full | 510.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.8 |
| dewey-search | 510.8 |
| dewey-sort | 3510.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn861692376 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:36Z |
| institution | BVB |
| isbn | 9781107088504 110708850X |
| language | English |
| oclc_num | 861692376 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xvii, 522 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Borceux, Francis, 1948- https://id.oclc.org/worldcat/entity/E39PBJqQvPRwXB3YBQmRkC3JDq http://id.loc.gov/authorities/names/n83129031 Handbook of categorical algebra 3 : categories of sheaves / Francis Borceux. Categories of sheaves Cambridge [England] ; New York : Cambridge University Press, [1994] ©1994 1 online resource (xvii, 522 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; volume 53 Includes bibliographical references (pages 514-516) and index. Print version record. 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 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 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 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. Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Algebra, Homological. http://id.loc.gov/authorities/subjects/sh85003432 Abelian categories. http://id.loc.gov/authorities/subjects/sh85000127 Catégories (Mathématiques) Algèbre homologique. Catégories abéliennes. MATHEMATICS Essays. bisacsh MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh Abelian categories fast Algebra, Homological fast Categories (Mathematics) fast Catégories (Mathématiques) ram Faisceaux, théorie des. ram Topos (Mathématiques) ram has work: Handbook of categorical algebra 3 Categories of sheaves (Text) https://id.oclc.org/worldcat/entity/E39PCFrPYtC9JQxRHwtFhvTtmm https://id.oclc.org/worldcat/ontology/hasWork Print version: Borceux, Francis, 1948- Handbook of categorical algebra 3 0521441803 (OCoLC)31978406 Encyclopedia of mathematics and its applications ; volume 53. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569273 Volltext |
| spellingShingle | Borceux, Francis, 1948- Handbook of categorical algebra 3 : categories of sheaves / Encyclopedia of mathematics and its applications ; 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 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 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 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Algebra, Homological. http://id.loc.gov/authorities/subjects/sh85003432 Abelian categories. http://id.loc.gov/authorities/subjects/sh85000127 Catégories (Mathématiques) Algèbre homologique. Catégories abéliennes. MATHEMATICS Essays. bisacsh MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh Abelian categories fast Algebra, Homological fast Categories (Mathematics) fast Catégories (Mathématiques) ram Faisceaux, théorie des. ram Topos (Mathématiques) ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85020992 http://id.loc.gov/authorities/subjects/sh85003432 http://id.loc.gov/authorities/subjects/sh85000127 |
| title | Handbook of categorical algebra 3 : categories of sheaves / |
| title_alt | Categories of sheaves |
| title_auth | Handbook of categorical algebra 3 : categories of sheaves / |
| title_exact_search | Handbook of categorical algebra 3 : categories of sheaves / |
| title_full | Handbook of categorical algebra 3 : categories of sheaves / Francis Borceux. |
| title_fullStr | Handbook of categorical algebra 3 : categories of sheaves / Francis Borceux. |
| title_full_unstemmed | Handbook of categorical algebra 3 : categories of sheaves / Francis Borceux. |
| title_short | Handbook of categorical algebra 3 : |
| title_sort | handbook of categorical algebra 3 categories of sheaves |
| title_sub | categories of sheaves / |
| topic | Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Algebra, Homological. http://id.loc.gov/authorities/subjects/sh85003432 Abelian categories. http://id.loc.gov/authorities/subjects/sh85000127 Catégories (Mathématiques) Algèbre homologique. Catégories abéliennes. MATHEMATICS Essays. bisacsh MATHEMATICS Pre-Calculus. bisacsh MATHEMATICS Reference. bisacsh Abelian categories fast Algebra, Homological fast Categories (Mathematics) fast Catégories (Mathématiques) ram Faisceaux, théorie des. ram Topos (Mathématiques) ram |
| topic_facet | Categories (Mathematics) Algebra, Homological. Abelian categories. Catégories (Mathématiques) Algèbre homologique. Catégories abéliennes. MATHEMATICS Essays. MATHEMATICS Pre-Calculus. MATHEMATICS Reference. Abelian categories Algebra, Homological Faisceaux, théorie des. Topos (Mathématiques) |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569273 |
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