Homological Algebra :: In Strongly Non-Abelian Settings.
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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Singapore :
World Scientific Pub. Co.,
2013.
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| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 2.2.3 Definition and Proposition (Exact ideals). |
| Beschreibung: | 1 online resource (356 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789814425926 9814425923 9814425915 9789814425919 9781299281301 1299281303 |
Internformat
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| 100 | 1 | |a Grandis, Marco. | |
| 245 | 1 | 0 | |a Homological Algebra : |b In Strongly Non-Abelian Settings. |
| 260 | |a Singapore : |b World Scientific Pub. Co., |c 2013. | ||
| 300 | |a 1 online resource (356 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 505 | 0 | |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). | |
| 500 | |a 2.2.3 Definition and Proposition (Exact ideals). | ||
| 520 | |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. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Algebra, Homological. |0 http://id.loc.gov/authorities/subjects/sh85003432 | |
| 650 | 0 | |a Homology theory. |0 http://id.loc.gov/authorities/subjects/sh85061770 | |
| 650 | 6 | |a Algèbre homologique. | |
| 650 | 6 | |a Homologie. | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a Algebra, Homological |2 fast | |
| 650 | 7 | |a Homology theory |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Grandis, Marco. |t Homological Algebra : In Strongly Non-Abelian Settings. |d Singapore : World Scientific Publishing Company, ©2013 |z 9789814425919 |
| 776 | 0 | 8 | |i Online version: |a Grandis, Marco. |t Homological Algebra. |d Singapore : World Scientific Pub. Co., 2013 |w (OCoLC)1102812182 |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn830162411 |
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| _version_ | 1816882225287790592 |
| adam_text | |
| any_adam_object | |
| author | Grandis, Marco |
| author_facet | Grandis, Marco |
| author_role | |
| author_sort | Grandis, Marco |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA169 |
| callnumber-raw | QA169 |
| callnumber-search | QA169 |
| callnumber-sort | QA 3169 |
| callnumber-subject | QA - Mathematics |
| 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). |
| ctrlnum | (OCoLC)830162411 |
| 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 | ZDB-4-EBA-ocn830162411 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:14Z |
| institution | BVB |
| isbn | 9789814425926 9814425923 9814425915 9789814425919 9781299281301 1299281303 |
| language | English |
| oclc_num | 830162411 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (356 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific Pub. Co., |
| record_format | marc |
| spelling | Grandis, Marco. Homological Algebra : In Strongly Non-Abelian Settings. Singapore : World Scientific Pub. Co., 2013. 1 online resource (356 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier 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). 2.2.3 Definition and Proposition (Exact ideals). 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. Print version record. Includes bibliographical references and index. English. Algebra, Homological. http://id.loc.gov/authorities/subjects/sh85003432 Homology theory. http://id.loc.gov/authorities/subjects/sh85061770 Algèbre homologique. Homologie. MATHEMATICS Group Theory. bisacsh Algebra, Homological fast Homology theory fast Print version: Grandis, Marco. Homological Algebra : In Strongly Non-Abelian Settings. Singapore : World Scientific Publishing Company, ©2013 9789814425919 Online version: Grandis, Marco. Homological Algebra. Singapore : World Scientific Pub. Co., 2013 (OCoLC)1102812182 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=545495 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). Algebra, Homological. http://id.loc.gov/authorities/subjects/sh85003432 Homology theory. http://id.loc.gov/authorities/subjects/sh85061770 Algèbre homologique. Homologie. MATHEMATICS Group Theory. bisacsh Algebra, Homological fast Homology theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85003432 http://id.loc.gov/authorities/subjects/sh85061770 |
| 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 | Algebra, Homological. http://id.loc.gov/authorities/subjects/sh85003432 Homology theory. http://id.loc.gov/authorities/subjects/sh85061770 Algèbre homologique. Homologie. MATHEMATICS Group Theory. bisacsh Algebra, Homological fast Homology theory fast |
| topic_facet | Algebra, Homological. Homology theory. Algèbre homologique. Homologie. MATHEMATICS Group Theory. Algebra, Homological Homology theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=545495 |
| work_keys_str_mv | AT grandismarco homologicalalgebrainstronglynonabeliansettings |