Homological Algebra: In Strongly Non-Abelian Settings
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
2013
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | 2.2.3 Definition and Proposition (Exact ideals) Print version record |
| Beschreibung: | 1 online resource (356 pages) |
| ISBN: | 9789814425926 9814425923 |
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| 100 | 1 | |a Grandis, Marco |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Homological Algebra |b In Strongly Non-Abelian Settings |
| 264 | 1 | |a Singapore |b World Scientific Pub. Co. |c 2013 | |
| 300 | |a 1 online resource (356 pages) | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b cr |2 rdacarrier | ||
| 500 | |a 2.2.3 Definition and Proposition (Exact ideals) | ||
| 500 | |a Print version record | ||
| 505 | 8 | |a Preface; Contents; Introduction; 0.1 Categorical settings for homological algebra; 0.2 Semiexact, homological and generalised exact categories; 0.3 Subquotients and homology; 0.4 Satellites; 0.5 Exact centres, expansions, fractions and relations; 0.6 Applications; 0.7 Homological theories and biuniversal models; 0.8 Modularity and additivity; 0.9 A list of examples; 0.10 Terminology and notation; 0.11 Acknowledgements; 1 Semiexact categories; 1.1 Some basic notions; 1.1.1 Lattices; 1.1.2 Distributive and modular lattices; 1.1.3 Galois connections; 1.1.4 Contravariant Galois connections | |
| 505 | 8 | |a 1.1.5 Isomorphisms, monomorphisms and epimorphisms1.1.6 Pointed categories; 1.1.7 Kernels and cokernels; 1.2 Lattices and Galois connections; 1.2.1 Definition; 1.2.2 Monos and epis; 1.2.3 Kernels and cokernels; 1.2.4 The normal factorisation; 1.2.5 Exact connections; 1.2.6 Normal monos and epis; 1.2.7 The semiadditive structure; 1.2.8 Modular connections; 1.3 The main definitions; 1.3.1 Ideals of null morphisms; 1.3.2 Closed ideals; 1.3.3 Semiexact categories; 1.3.4 Remarks; 1.3.5 Kernel duality and short exact sequences; 1.3.6 Homological and generalised exact categories; 1.3.7 Subcategories | |
| 505 | 8 | |a 1.4 Structural examples1.4.1 Lattices and connections; 1.4.2 A basic homological category; 1.4.3 A p-exact category; 1.4.4 Graded objects; 1.4.5 The canonical enriched structure; 1.4.6 Proposition; 1.5 Semiexact categories and normal subobjects; 1.5.1 Semiexact categories and local smallness; 1.5.2 Exact sequences; 1.5.3 Lemma (Annihilation properties); 1.5.4 Theorem (Two criteria for semiexact categories); 1.5.5 Normal factorisations and exact morphisms; 1.5.6 Direct and inverse images; 1.5.7 Lemma (Meets and detection properties); 1.5.8 Theorem and Definition (The transfer functor) | |
| 505 | 8 | |a 1.5.9 Remarks1.6 Other examples of semiexact and homological categories; 1.6.1 Groups, rings and groupoids; 1.6.2 Abelian monoids, semimodules, preordered abelian groups; 1.6.3 Topological vector spaces; 1.6.4 Pointed sets and spaces; 1.6.5 Categories of partial mappings; 1.6.6 General modules; 1.6.7 Categories of pairs; 1.6.8 Groups as pairs; 1.6.9 Two examples; 1.7 Exact functors; 1.7.0 Basic definitions; 1.7.1 Exact functors and normal subobjects; 1.7.2 Conservative exact functors; 1.7.3 Proposition and Definition (Semiexact subcategories); 1.7.4 Examples | |
| 505 | 8 | |a 1.7.5 Left exact functors and right adjoints1.7.6 Categories of maps and kernel functors; 1.7.7 Categories of functors; 1.7.8 Pseudolimits in EX1; 1.7.9 Proposition (Closed ideals and adjunctions); 2 Homological categories; 2.1 The transfer functor and ex2-categories; 2.1.1 Fully normal monos and epis; 2.1.2 Theorem (Exactness properties of the transfer functor); 2.1.3 Ex2-categories; 2.1.4 The associated projective category; 2.2 Characterisations of homological and g-exact categories; 2.2.1 Lemma (The special 3×3-lemma); 2.2.2 Theorem (Homological categories) | |
| 505 | 8 | |a We propose here a study of 'semiexact' and 'homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied. This is a sequel of a book on 'Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups', published by the same Editor, but can be read independently of the latter. The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell - a modera | |
| 650 | 7 | |a MATHEMATICS / Group Theory |2 bisacsh | |
| 650 | 7 | |a Algebra, Homological |2 fast | |
| 650 | 7 | |a Homology theory |2 fast | |
| 650 | 4 | |a Algebra, Homological | |
| 650 | 4 | |a Homology theory | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |a Grandis, Marco |t Homological Algebra : In Strongly Non-Abelian Settings |
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Datensatz im Suchindex
| _version_ | 1804175392722911232 |
|---|---|
| any_adam_object | |
| author | Grandis, Marco |
| author_facet | Grandis, Marco |
| author_role | aut |
| author_sort | Grandis, Marco |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | BV043034120 |
| collection | ZDB-4-EBA |
| contents | Preface; Contents; Introduction; 0.1 Categorical settings for homological algebra; 0.2 Semiexact, homological and generalised exact categories; 0.3 Subquotients and homology; 0.4 Satellites; 0.5 Exact centres, expansions, fractions and relations; 0.6 Applications; 0.7 Homological theories and biuniversal models; 0.8 Modularity and additivity; 0.9 A list of examples; 0.10 Terminology and notation; 0.11 Acknowledgements; 1 Semiexact categories; 1.1 Some basic notions; 1.1.1 Lattices; 1.1.2 Distributive and modular lattices; 1.1.3 Galois connections; 1.1.4 Contravariant Galois connections 1.1.5 Isomorphisms, monomorphisms and epimorphisms1.1.6 Pointed categories; 1.1.7 Kernels and cokernels; 1.2 Lattices and Galois connections; 1.2.1 Definition; 1.2.2 Monos and epis; 1.2.3 Kernels and cokernels; 1.2.4 The normal factorisation; 1.2.5 Exact connections; 1.2.6 Normal monos and epis; 1.2.7 The semiadditive structure; 1.2.8 Modular connections; 1.3 The main definitions; 1.3.1 Ideals of null morphisms; 1.3.2 Closed ideals; 1.3.3 Semiexact categories; 1.3.4 Remarks; 1.3.5 Kernel duality and short exact sequences; 1.3.6 Homological and generalised exact categories; 1.3.7 Subcategories 1.4 Structural examples1.4.1 Lattices and connections; 1.4.2 A basic homological category; 1.4.3 A p-exact category; 1.4.4 Graded objects; 1.4.5 The canonical enriched structure; 1.4.6 Proposition; 1.5 Semiexact categories and normal subobjects; 1.5.1 Semiexact categories and local smallness; 1.5.2 Exact sequences; 1.5.3 Lemma (Annihilation properties); 1.5.4 Theorem (Two criteria for semiexact categories); 1.5.5 Normal factorisations and exact morphisms; 1.5.6 Direct and inverse images; 1.5.7 Lemma (Meets and detection properties); 1.5.8 Theorem and Definition (The transfer functor) 1.5.9 Remarks1.6 Other examples of semiexact and homological categories; 1.6.1 Groups, rings and groupoids; 1.6.2 Abelian monoids, semimodules, preordered abelian groups; 1.6.3 Topological vector spaces; 1.6.4 Pointed sets and spaces; 1.6.5 Categories of partial mappings; 1.6.6 General modules; 1.6.7 Categories of pairs; 1.6.8 Groups as pairs; 1.6.9 Two examples; 1.7 Exact functors; 1.7.0 Basic definitions; 1.7.1 Exact functors and normal subobjects; 1.7.2 Conservative exact functors; 1.7.3 Proposition and Definition (Semiexact subcategories); 1.7.4 Examples 1.7.5 Left exact functors and right adjoints1.7.6 Categories of maps and kernel functors; 1.7.7 Categories of functors; 1.7.8 Pseudolimits in EX1; 1.7.9 Proposition (Closed ideals and adjunctions); 2 Homological categories; 2.1 The transfer functor and ex2-categories; 2.1.1 Fully normal monos and epis; 2.1.2 Theorem (Exactness properties of the transfer functor); 2.1.3 Ex2-categories; 2.1.4 The associated projective category; 2.2 Characterisations of homological and g-exact categories; 2.2.1 Lemma (The special 3×3-lemma); 2.2.2 Theorem (Homological categories) We propose here a study of 'semiexact' and 'homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied. This is a sequel of a book on 'Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups', published by the same Editor, but can be read independently of the latter. The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell - a modera |
| ctrlnum | (OCoLC)830162411 (DE-599)BVBBV043034120 |
| dewey-full | 512.25 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.25 |
| dewey-search | 512.25 |
| dewey-sort | 3512.25 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043034120 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:34Z |
| institution | BVB |
| isbn | 9789814425926 9814425923 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028458768 |
| oclc_num | 830162411 |
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| physical | 1 online resource (356 pages) |
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| spelling | Grandis, Marco Verfasser aut Homological Algebra In Strongly Non-Abelian Settings Singapore World Scientific Pub. Co. 2013 1 online resource (356 pages) txt rdacontent c rdamedia cr rdacarrier 2.2.3 Definition and Proposition (Exact ideals) Print version record Preface; Contents; Introduction; 0.1 Categorical settings for homological algebra; 0.2 Semiexact, homological and generalised exact categories; 0.3 Subquotients and homology; 0.4 Satellites; 0.5 Exact centres, expansions, fractions and relations; 0.6 Applications; 0.7 Homological theories and biuniversal models; 0.8 Modularity and additivity; 0.9 A list of examples; 0.10 Terminology and notation; 0.11 Acknowledgements; 1 Semiexact categories; 1.1 Some basic notions; 1.1.1 Lattices; 1.1.2 Distributive and modular lattices; 1.1.3 Galois connections; 1.1.4 Contravariant Galois connections 1.1.5 Isomorphisms, monomorphisms and epimorphisms1.1.6 Pointed categories; 1.1.7 Kernels and cokernels; 1.2 Lattices and Galois connections; 1.2.1 Definition; 1.2.2 Monos and epis; 1.2.3 Kernels and cokernels; 1.2.4 The normal factorisation; 1.2.5 Exact connections; 1.2.6 Normal monos and epis; 1.2.7 The semiadditive structure; 1.2.8 Modular connections; 1.3 The main definitions; 1.3.1 Ideals of null morphisms; 1.3.2 Closed ideals; 1.3.3 Semiexact categories; 1.3.4 Remarks; 1.3.5 Kernel duality and short exact sequences; 1.3.6 Homological and generalised exact categories; 1.3.7 Subcategories 1.4 Structural examples1.4.1 Lattices and connections; 1.4.2 A basic homological category; 1.4.3 A p-exact category; 1.4.4 Graded objects; 1.4.5 The canonical enriched structure; 1.4.6 Proposition; 1.5 Semiexact categories and normal subobjects; 1.5.1 Semiexact categories and local smallness; 1.5.2 Exact sequences; 1.5.3 Lemma (Annihilation properties); 1.5.4 Theorem (Two criteria for semiexact categories); 1.5.5 Normal factorisations and exact morphisms; 1.5.6 Direct and inverse images; 1.5.7 Lemma (Meets and detection properties); 1.5.8 Theorem and Definition (The transfer functor) 1.5.9 Remarks1.6 Other examples of semiexact and homological categories; 1.6.1 Groups, rings and groupoids; 1.6.2 Abelian monoids, semimodules, preordered abelian groups; 1.6.3 Topological vector spaces; 1.6.4 Pointed sets and spaces; 1.6.5 Categories of partial mappings; 1.6.6 General modules; 1.6.7 Categories of pairs; 1.6.8 Groups as pairs; 1.6.9 Two examples; 1.7 Exact functors; 1.7.0 Basic definitions; 1.7.1 Exact functors and normal subobjects; 1.7.2 Conservative exact functors; 1.7.3 Proposition and Definition (Semiexact subcategories); 1.7.4 Examples 1.7.5 Left exact functors and right adjoints1.7.6 Categories of maps and kernel functors; 1.7.7 Categories of functors; 1.7.8 Pseudolimits in EX1; 1.7.9 Proposition (Closed ideals and adjunctions); 2 Homological categories; 2.1 The transfer functor and ex2-categories; 2.1.1 Fully normal monos and epis; 2.1.2 Theorem (Exactness properties of the transfer functor); 2.1.3 Ex2-categories; 2.1.4 The associated projective category; 2.2 Characterisations of homological and g-exact categories; 2.2.1 Lemma (The special 3×3-lemma); 2.2.2 Theorem (Homological categories) We propose here a study of 'semiexact' and 'homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied. This is a sequel of a book on 'Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups', published by the same Editor, but can be read independently of the latter. The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell - a modera MATHEMATICS / Group Theory bisacsh Algebra, Homological fast Homology theory fast Algebra, Homological Homology theory Erscheint auch als Druck-Ausgabe Grandis, Marco Homological Algebra : In Strongly Non-Abelian Settings http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=545495 Aggregator Volltext |
| spellingShingle | Grandis, Marco Homological Algebra In Strongly Non-Abelian Settings Preface; Contents; Introduction; 0.1 Categorical settings for homological algebra; 0.2 Semiexact, homological and generalised exact categories; 0.3 Subquotients and homology; 0.4 Satellites; 0.5 Exact centres, expansions, fractions and relations; 0.6 Applications; 0.7 Homological theories and biuniversal models; 0.8 Modularity and additivity; 0.9 A list of examples; 0.10 Terminology and notation; 0.11 Acknowledgements; 1 Semiexact categories; 1.1 Some basic notions; 1.1.1 Lattices; 1.1.2 Distributive and modular lattices; 1.1.3 Galois connections; 1.1.4 Contravariant Galois connections 1.1.5 Isomorphisms, monomorphisms and epimorphisms1.1.6 Pointed categories; 1.1.7 Kernels and cokernels; 1.2 Lattices and Galois connections; 1.2.1 Definition; 1.2.2 Monos and epis; 1.2.3 Kernels and cokernels; 1.2.4 The normal factorisation; 1.2.5 Exact connections; 1.2.6 Normal monos and epis; 1.2.7 The semiadditive structure; 1.2.8 Modular connections; 1.3 The main definitions; 1.3.1 Ideals of null morphisms; 1.3.2 Closed ideals; 1.3.3 Semiexact categories; 1.3.4 Remarks; 1.3.5 Kernel duality and short exact sequences; 1.3.6 Homological and generalised exact categories; 1.3.7 Subcategories 1.4 Structural examples1.4.1 Lattices and connections; 1.4.2 A basic homological category; 1.4.3 A p-exact category; 1.4.4 Graded objects; 1.4.5 The canonical enriched structure; 1.4.6 Proposition; 1.5 Semiexact categories and normal subobjects; 1.5.1 Semiexact categories and local smallness; 1.5.2 Exact sequences; 1.5.3 Lemma (Annihilation properties); 1.5.4 Theorem (Two criteria for semiexact categories); 1.5.5 Normal factorisations and exact morphisms; 1.5.6 Direct and inverse images; 1.5.7 Lemma (Meets and detection properties); 1.5.8 Theorem and Definition (The transfer functor) 1.5.9 Remarks1.6 Other examples of semiexact and homological categories; 1.6.1 Groups, rings and groupoids; 1.6.2 Abelian monoids, semimodules, preordered abelian groups; 1.6.3 Topological vector spaces; 1.6.4 Pointed sets and spaces; 1.6.5 Categories of partial mappings; 1.6.6 General modules; 1.6.7 Categories of pairs; 1.6.8 Groups as pairs; 1.6.9 Two examples; 1.7 Exact functors; 1.7.0 Basic definitions; 1.7.1 Exact functors and normal subobjects; 1.7.2 Conservative exact functors; 1.7.3 Proposition and Definition (Semiexact subcategories); 1.7.4 Examples 1.7.5 Left exact functors and right adjoints1.7.6 Categories of maps and kernel functors; 1.7.7 Categories of functors; 1.7.8 Pseudolimits in EX1; 1.7.9 Proposition (Closed ideals and adjunctions); 2 Homological categories; 2.1 The transfer functor and ex2-categories; 2.1.1 Fully normal monos and epis; 2.1.2 Theorem (Exactness properties of the transfer functor); 2.1.3 Ex2-categories; 2.1.4 The associated projective category; 2.2 Characterisations of homological and g-exact categories; 2.2.1 Lemma (The special 3×3-lemma); 2.2.2 Theorem (Homological categories) We propose here a study of 'semiexact' and 'homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied. This is a sequel of a book on 'Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups', published by the same Editor, but can be read independently of the latter. The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell - a modera MATHEMATICS / Group Theory bisacsh Algebra, Homological fast Homology theory fast Algebra, Homological Homology theory |
| title | Homological Algebra In Strongly Non-Abelian Settings |
| title_auth | Homological Algebra In Strongly Non-Abelian Settings |
| title_exact_search | Homological Algebra In Strongly Non-Abelian Settings |
| title_full | Homological Algebra In Strongly Non-Abelian Settings |
| title_fullStr | Homological Algebra In Strongly Non-Abelian Settings |
| title_full_unstemmed | Homological Algebra In Strongly Non-Abelian Settings |
| title_short | Homological Algebra |
| title_sort | homological algebra in strongly non abelian settings |
| title_sub | In Strongly Non-Abelian Settings |
| topic | MATHEMATICS / Group Theory bisacsh Algebra, Homological fast Homology theory fast Algebra, Homological Homology theory |
| topic_facet | MATHEMATICS / Group Theory Algebra, Homological Homology theory |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=545495 |
| work_keys_str_mv | AT grandismarco homologicalalgebrainstronglynonabeliansettings |