Handbook of categorical algebra 2 :: categories and structures /
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. The volumes are written in sequence. The second, which assumes familiarity with the materia...
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 ;
51. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users. |
| Beschreibung: | 1 online resource (xvii, 443 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 436-438) and index. |
| ISBN: | 9781461941453 1461941458 9780511525865 0511525869 9781139881975 1139881973 |
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| 245 | 1 | 0 | |a Handbook of categorical algebra 2 : |b categories and structures / |c Francis Borceux. |
| 264 | 1 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c [1994] | |
| 264 | 4 | |c ©1994 | |
| 300 | |a 1 online resource (xvii, 443 pages) : |b illustrations | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v 51 | |
| 504 | |a Includes bibliographical references (pages 436-438) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users. | ||
| 505 | 0 | |a Cover; Half-title; Title; Copyright; Dedication; Contents; Preface to volume 2; Introduction to this handbook; 1 Abelian categories; 1.1 Zero objects and kernels; 1.2 Additive categories and biproducts; 1.3 Additive functors; 1.4 Abelian categories; 1.5 Exactness properties of abelian categories; 1.6 Additivity of abelian categories; 1.7 Union of subobjects; 1.8 Exact sequences; 1.9 Diagram chasing; 1.10 Some diagram lemmas; 1.11 Exact functors; 1.12 Torsion theories; 1.13 Localizations of abelian categories; 1.14 The embedding theorem; 1.15 Exercises; 2 Regular categories | |
| 505 | 8 | |a 2.1 Exactness properties of regular categories2.2 Definition in terms of strong epimorphisms; 2.3 Exact sequences; 2.4 Examples; 2.5 Equivalence relations; 2.6 Exact categories; 2.7 An embedding theorem; 2.8 The calculus of relations; 2.9 Exercises; 3 Algebraic theories; 3.1 The theory of groups revisited; 3.2 A glance at universal algebra; 3.3 A categorical approach to universal algebra; 3.4 Limits and colimits in algebraic categories; 3.5 The exactness properties of algebraic categories; 3.6 The algebraic lattices of subobjects; 3.7 Algebraic functors; 3.8 Freely generated models | |
| 505 | 8 | |a 3.9 Characterization of algebraic categories3.10 Commutative theories; 3.11 Tensor product of theories; 3.12 A glance at Morita theory; 3.13 Exercises; 4 Monads; 4.1 Monads and their algebras; 4.2 Monads and adjunctions; 4.3 Limits and colimits in categories of algebras; 4.4 Characterization of monadic categories; 4.5 The adjoint lifting theorem; 4.6 Monads with rank; 4.7 A glance at descent theory; 4.8 Exercises; 5 Accessible categories; 5.1 Presentable objects in a category; 5.2 Locally presentable categories; 5.3 Accessible categories; 5.4 Raising the degree of accessibility | |
| 505 | 8 | |a 5.5 Functors with rank5.6 Sketches; 5.7 Exercises; 6 Enriched category theory; 6.1 Symmetric monoidal closed categories; 6.2 Enriched categories; 6.3 The enriched Yoneda lemma; 6.4 Change of base; 6.5 Tensors and cotensors; 6.6 Weighted limits; 6.7 Enriched adjunctions; 6.8 Exercises; 7 Topological categories; 7.1 Exponentiable spaces; 7.2 Compactly generated spaces; 7.3 Topological functors; 7.4 Exercises; 8 Fibred categories; 8.1 Fibrations; 8.2 Cartesian functors; 8.3 Fibrations via pseudo-functors; 8.4 Fibred adjunctions; 8.5 Completeness of a fibration; 8.6 Locally small fibrations | |
| 505 | 8 | |a 8.7 Definability8.8 Exercises; Bibliography; Index | |
| 650 | 0 | |a Categories (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85020992 | |
| 650 | 0 | |a Algebra, Homological. |0 http://id.loc.gov/authorities/subjects/sh85003432 | |
| 650 | 0 | |a Abelian categories. |0 http://id.loc.gov/authorities/subjects/sh85000127 | |
| 650 | 6 | |a Catégories (Mathématiques) | |
| 650 | 6 | |a Algèbre homologique. | |
| 650 | 6 | |a Catégories abéliennes. | |
| 650 | 7 | |a MATHEMATICS |x Essays. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Pre-Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Reference. |2 bisacsh | |
| 650 | 7 | |a Abelian categories |2 fast | |
| 650 | 7 | |a Algebra, Homological |2 fast | |
| 650 | 7 | |a Categories (Mathematics) |2 fast | |
| 650 | 7 | |a Catégories (mathématiques) |2 ram | |
| 650 | 7 | |a Algèbre homologique. |2 ram | |
| 650 | 7 | |a Catégories abéliennes. |2 ram | |
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| author | Borceux, Francis, 1948- |
| author_GND | http://id.loc.gov/authorities/names/n83129031 |
| author_facet | Borceux, Francis, 1948- |
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| author_sort | Borceux, Francis, 1948- |
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| contents | Cover; Half-title; Title; Copyright; Dedication; Contents; Preface to volume 2; Introduction to this handbook; 1 Abelian categories; 1.1 Zero objects and kernels; 1.2 Additive categories and biproducts; 1.3 Additive functors; 1.4 Abelian categories; 1.5 Exactness properties of abelian categories; 1.6 Additivity of abelian categories; 1.7 Union of subobjects; 1.8 Exact sequences; 1.9 Diagram chasing; 1.10 Some diagram lemmas; 1.11 Exact functors; 1.12 Torsion theories; 1.13 Localizations of abelian categories; 1.14 The embedding theorem; 1.15 Exercises; 2 Regular categories 2.1 Exactness properties of regular categories2.2 Definition in terms of strong epimorphisms; 2.3 Exact sequences; 2.4 Examples; 2.5 Equivalence relations; 2.6 Exact categories; 2.7 An embedding theorem; 2.8 The calculus of relations; 2.9 Exercises; 3 Algebraic theories; 3.1 The theory of groups revisited; 3.2 A glance at universal algebra; 3.3 A categorical approach to universal algebra; 3.4 Limits and colimits in algebraic categories; 3.5 The exactness properties of algebraic categories; 3.6 The algebraic lattices of subobjects; 3.7 Algebraic functors; 3.8 Freely generated models 3.9 Characterization of algebraic categories3.10 Commutative theories; 3.11 Tensor product of theories; 3.12 A glance at Morita theory; 3.13 Exercises; 4 Monads; 4.1 Monads and their algebras; 4.2 Monads and adjunctions; 4.3 Limits and colimits in categories of algebras; 4.4 Characterization of monadic categories; 4.5 The adjoint lifting theorem; 4.6 Monads with rank; 4.7 A glance at descent theory; 4.8 Exercises; 5 Accessible categories; 5.1 Presentable objects in a category; 5.2 Locally presentable categories; 5.3 Accessible categories; 5.4 Raising the degree of accessibility 5.5 Functors with rank5.6 Sketches; 5.7 Exercises; 6 Enriched category theory; 6.1 Symmetric monoidal closed categories; 6.2 Enriched categories; 6.3 The enriched Yoneda lemma; 6.4 Change of base; 6.5 Tensors and cotensors; 6.6 Weighted limits; 6.7 Enriched adjunctions; 6.8 Exercises; 7 Topological categories; 7.1 Exponentiable spaces; 7.2 Compactly generated spaces; 7.3 Topological functors; 7.4 Exercises; 8 Fibred categories; 8.1 Fibrations; 8.2 Cartesian functors; 8.3 Fibrations via pseudo-functors; 8.4 Fibred adjunctions; 8.5 Completeness of a fibration; 8.6 Locally small fibrations 8.7 Definability8.8 Exercises; Bibliography; Index |
| ctrlnum | (OCoLC)857769774 |
| 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-ocn857769774 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:31Z |
| institution | BVB |
| isbn | 9781461941453 1461941458 9780511525865 0511525869 9781139881975 1139881973 |
| language | English |
| oclc_num | 857769774 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xvii, 443 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 2 : categories and structures / Francis Borceux. Cambridge [England] ; New York : Cambridge University Press, [1994] ©1994 1 online resource (xvii, 443 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; 51 Includes bibliographical references (pages 436-438) and index. Print version record. 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. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users. Cover; Half-title; Title; Copyright; Dedication; Contents; Preface to volume 2; Introduction to this handbook; 1 Abelian categories; 1.1 Zero objects and kernels; 1.2 Additive categories and biproducts; 1.3 Additive functors; 1.4 Abelian categories; 1.5 Exactness properties of abelian categories; 1.6 Additivity of abelian categories; 1.7 Union of subobjects; 1.8 Exact sequences; 1.9 Diagram chasing; 1.10 Some diagram lemmas; 1.11 Exact functors; 1.12 Torsion theories; 1.13 Localizations of abelian categories; 1.14 The embedding theorem; 1.15 Exercises; 2 Regular categories 2.1 Exactness properties of regular categories2.2 Definition in terms of strong epimorphisms; 2.3 Exact sequences; 2.4 Examples; 2.5 Equivalence relations; 2.6 Exact categories; 2.7 An embedding theorem; 2.8 The calculus of relations; 2.9 Exercises; 3 Algebraic theories; 3.1 The theory of groups revisited; 3.2 A glance at universal algebra; 3.3 A categorical approach to universal algebra; 3.4 Limits and colimits in algebraic categories; 3.5 The exactness properties of algebraic categories; 3.6 The algebraic lattices of subobjects; 3.7 Algebraic functors; 3.8 Freely generated models 3.9 Characterization of algebraic categories3.10 Commutative theories; 3.11 Tensor product of theories; 3.12 A glance at Morita theory; 3.13 Exercises; 4 Monads; 4.1 Monads and their algebras; 4.2 Monads and adjunctions; 4.3 Limits and colimits in categories of algebras; 4.4 Characterization of monadic categories; 4.5 The adjoint lifting theorem; 4.6 Monads with rank; 4.7 A glance at descent theory; 4.8 Exercises; 5 Accessible categories; 5.1 Presentable objects in a category; 5.2 Locally presentable categories; 5.3 Accessible categories; 5.4 Raising the degree of accessibility 5.5 Functors with rank5.6 Sketches; 5.7 Exercises; 6 Enriched category theory; 6.1 Symmetric monoidal closed categories; 6.2 Enriched categories; 6.3 The enriched Yoneda lemma; 6.4 Change of base; 6.5 Tensors and cotensors; 6.6 Weighted limits; 6.7 Enriched adjunctions; 6.8 Exercises; 7 Topological categories; 7.1 Exponentiable spaces; 7.2 Compactly generated spaces; 7.3 Topological functors; 7.4 Exercises; 8 Fibred categories; 8.1 Fibrations; 8.2 Cartesian functors; 8.3 Fibrations via pseudo-functors; 8.4 Fibred adjunctions; 8.5 Completeness of a fibration; 8.6 Locally small fibrations 8.7 Definability8.8 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 Algèbre homologique. ram Catégories abéliennes. ram has work: 2 Categories and structures Handbook of categorical algebra (Text) https://id.oclc.org/worldcat/entity/E39PCGT47PfrjPK9XfVqxg7tfC https://id.oclc.org/worldcat/ontology/hasWork Print version: Borceux, Francis, 1948- Handbook of categorical algebra 2 052144179X (OCoLC)31907549 Encyclopedia of mathematics and its applications ; 51. 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=616987 Volltext |
| spellingShingle | Borceux, Francis, 1948- Handbook of categorical algebra 2 : categories and structures / Encyclopedia of mathematics and its applications ; Cover; Half-title; Title; Copyright; Dedication; Contents; Preface to volume 2; Introduction to this handbook; 1 Abelian categories; 1.1 Zero objects and kernels; 1.2 Additive categories and biproducts; 1.3 Additive functors; 1.4 Abelian categories; 1.5 Exactness properties of abelian categories; 1.6 Additivity of abelian categories; 1.7 Union of subobjects; 1.8 Exact sequences; 1.9 Diagram chasing; 1.10 Some diagram lemmas; 1.11 Exact functors; 1.12 Torsion theories; 1.13 Localizations of abelian categories; 1.14 The embedding theorem; 1.15 Exercises; 2 Regular categories 2.1 Exactness properties of regular categories2.2 Definition in terms of strong epimorphisms; 2.3 Exact sequences; 2.4 Examples; 2.5 Equivalence relations; 2.6 Exact categories; 2.7 An embedding theorem; 2.8 The calculus of relations; 2.9 Exercises; 3 Algebraic theories; 3.1 The theory of groups revisited; 3.2 A glance at universal algebra; 3.3 A categorical approach to universal algebra; 3.4 Limits and colimits in algebraic categories; 3.5 The exactness properties of algebraic categories; 3.6 The algebraic lattices of subobjects; 3.7 Algebraic functors; 3.8 Freely generated models 3.9 Characterization of algebraic categories3.10 Commutative theories; 3.11 Tensor product of theories; 3.12 A glance at Morita theory; 3.13 Exercises; 4 Monads; 4.1 Monads and their algebras; 4.2 Monads and adjunctions; 4.3 Limits and colimits in categories of algebras; 4.4 Characterization of monadic categories; 4.5 The adjoint lifting theorem; 4.6 Monads with rank; 4.7 A glance at descent theory; 4.8 Exercises; 5 Accessible categories; 5.1 Presentable objects in a category; 5.2 Locally presentable categories; 5.3 Accessible categories; 5.4 Raising the degree of accessibility 5.5 Functors with rank5.6 Sketches; 5.7 Exercises; 6 Enriched category theory; 6.1 Symmetric monoidal closed categories; 6.2 Enriched categories; 6.3 The enriched Yoneda lemma; 6.4 Change of base; 6.5 Tensors and cotensors; 6.6 Weighted limits; 6.7 Enriched adjunctions; 6.8 Exercises; 7 Topological categories; 7.1 Exponentiable spaces; 7.2 Compactly generated spaces; 7.3 Topological functors; 7.4 Exercises; 8 Fibred categories; 8.1 Fibrations; 8.2 Cartesian functors; 8.3 Fibrations via pseudo-functors; 8.4 Fibred adjunctions; 8.5 Completeness of a fibration; 8.6 Locally small fibrations 8.7 Definability8.8 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 Algèbre homologique. ram Catégories abéliennes. 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 2 : categories and structures / |
| title_auth | Handbook of categorical algebra 2 : categories and structures / |
| title_exact_search | Handbook of categorical algebra 2 : categories and structures / |
| title_full | Handbook of categorical algebra 2 : categories and structures / Francis Borceux. |
| title_fullStr | Handbook of categorical algebra 2 : categories and structures / Francis Borceux. |
| title_full_unstemmed | Handbook of categorical algebra 2 : categories and structures / Francis Borceux. |
| title_short | Handbook of categorical algebra 2 : |
| title_sort | handbook of categorical algebra 2 categories and structures |
| title_sub | categories and structures / |
| 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 Algèbre homologique. ram Catégories abéliennes. 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 Catégories (mathématiques) |
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