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Homological algebra [[electronic resource] ] : in strongly non-Abelian settings / / Marco Grandis
| Homological algebra [[electronic resource] ] : in strongly non-Abelian settings / / Marco Grandis |
| Autore | Grandis Marco |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2013 |
| Descrizione fisica | 1 online resource (356 p.) |
| Disciplina | 512.64 |
| Soggetto topico |
Algebra, Homological
Homology theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-299-28130-3
981-4425-92-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 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 semi-additive 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 examples 1.4.1 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 Semi-exact categories and normal subobjects; 1.5.1 Semi-exact categories and local smallness; 1.5.2 Exact sequences; 1.5.3 Lemma (Annihilation properties); 1.5.4 Theorem (Two criteria for semi-exact 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 Remarks 1.6 Other examples of semi-exact 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 2.2.3 Definition and Proposition (Exact ideals) |
| Record Nr. | UNINA-9910465423503321 |
Grandis Marco
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Homological algebra : in strongly non-Abelian settings / / Marco Grandis, Universita di Genova, Italy
| Homological algebra : in strongly non-Abelian settings / / Marco Grandis, Universita di Genova, Italy |
| Autore | Grandis Marco |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2013 |
| Descrizione fisica | 1 online resource (xi, 343 pages) : illustrations |
| Disciplina | 512.64 |
| Collana | Gale eBooks |
| Soggetto topico |
Algebra, Homological
Homology theory |
| ISBN |
1-299-28130-3
981-4425-92-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 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 semi-additive 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 examples 1.4.1 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 Semi-exact categories and normal subobjects; 1.5.1 Semi-exact categories and local smallness; 1.5.2 Exact sequences; 1.5.3 Lemma (Annihilation properties); 1.5.4 Theorem (Two criteria for semi-exact 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 Remarks 1.6 Other examples of semi-exact 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 2.2.3 Definition and Proposition (Exact ideals) |
| Record Nr. | UNINA-9910792054003321 |
|
Grandis Marco
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Homological algebra : in strongly non-Abelian settings / / Marco Grandis, Universita di Genova, Italy
| Homological algebra : in strongly non-Abelian settings / / Marco Grandis, Universita di Genova, Italy |
| Autore | Grandis Marco |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2013 |
| Descrizione fisica | 1 online resource (xi, 343 pages) : illustrations |
| Disciplina | 512.64 |
| Collana | Gale eBooks |
| Soggetto topico |
Algebra, Homological
Homology theory |
| ISBN |
1-299-28130-3
981-4425-92-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 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 semi-additive 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 examples 1.4.1 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 Semi-exact categories and normal subobjects; 1.5.1 Semi-exact categories and local smallness; 1.5.2 Exact sequences; 1.5.3 Lemma (Annihilation properties); 1.5.4 Theorem (Two criteria for semi-exact 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 Remarks 1.6 Other examples of semi-exact 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 2.2.3 Definition and Proposition (Exact ideals) |
| Record Nr. | UNINA-9910826773403321 |
|
Grandis Marco
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Homological algebra [[electronic resource] ] : the interplay of homology with distributive lattices and orthodox semigroups / / Marco Grandis
| Homological algebra [[electronic resource] ] : the interplay of homology with distributive lattices and orthodox semigroups / / Marco Grandis |
| Autore | Grandis Marco |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (382 p.) |
| Disciplina | 512/.55 |
| Soggetto topico | Algebra, Homological |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-60370-8
9786613784391 981-4407-07-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; Introduction; 0.1 Homological algebra in a non-abelian setting; 0.2 The coherence problem for subquotients; 0.3 The transfer functor; 0.4 Distributivity and coherence; 0.5 Universal models and crossword chasing; 0.6 Outline; 0.7 Further extensions; 0.8 Literature and terminology; 0.9 Acknowledgements; 1 Coherence and models in homological algebra; 1.1 Some basic notions; 1.1.1 Monomorphisms and epimorphisms; 1.1.2 Lattices; 1.1.3 Distributive and modular lattices; 1.2 Coherence and distributive lattices; 1.2.1 Subquotients and regular induction
1.2.2 Relations of abelian groups1.2.3 Induced relations and canonical isomorphisms; 1.2.4 Examples of incoherence; 1.2.5 Coherent systems of isomorphisms; 1.2.6 Lemma; 1.2.7 Coherence Theorem of homological algebra (Reduced form); 1.3 Coherence and crossword diagrams; 1.3.1 Representing a bifiltered object; 1.3.2 Extending the representation; 1.3.3 Preparing a further extension; 1.3.4 The complete representation; 1.3.5 The Jordan-Holder Theorem; 1.3.6 Representing a sequence of morphisms; 1.4 Coherence and representations of spectral sequences 1.4.1 The universal model of the filtered complex1.4.2 The spectral sequence; 1.4.3 The spectral sequence, continued; 1.4.4 Transgressions; 1.4.5 A non-distributive structure; 1.5 Introducing p-exact categories; 1.5.1 Some terminology; 1.5.2 Pointed categories; 1.5.3 Kernels and cokernels; 1.5.4 Exact categories and exact functors; 1.5.5 Smallness; 1.5.6 Examples; 1.5.7 Galois connections; 1.5.8 Modular lattices and modular connections; 1.6 A synopsis of the projective approach; 1.6.1 Direct and inverse images of abelian groups; 1.6.2 The transfer functor; 1.6.3 Distributivity and coherence 1.6.4 The category of sets and partial bijections1.6.5 Generalisations; 1.7 Free modular lattices; 1.7.1 The Birkhoff Theorem (finite case); 1.7.2 The Birkhoff Theorem (general case); 2 Puppe-exact categories; 2.1 Abelian and p-exact categories; 2.1.1 Additive categories and biproducts; 2.1.2 Lemma (Biproducts); 2.1.3 Theorem and Definition (Semiadditive categories); 2.1.4 Additive categories; 2.1.5 Theorem and definition (Abelian categories); 2.1.6 Biproducts in abelian categories; 2.1.7 Split products in p-exact categories; 2.1.8 Examples of split products 2.1.9 Split products and abelian-valued functors2.2 Subobjects, quotients and the transfer functor; 2.2.1 Kernel duality; 2.2.2 Exact sequences; 2.2.3 Theorem (Modular lattices); 2.2.4 Lemma (Pullbacks and pushouts in p-exact categories); 2.2.5 Direct and inverse images; 2.2.6 Theorem and Definition (The transfer functor); 2.2.7 Subquotients; 2.2.8 Further remarks on modular lattices; 2.2.9 Lemma (Noether isomorphisms); 2.3 Projective p-exact categories and projective spaces; 2.3.1 The associated projective category; 2.3.2 Proposition (The projective congruence of vector spaces) 2.3.3 Projective spaces and projective maps |
| Record Nr. | UNINA-9910462552203321 |
|
Grandis Marco
|
||
| Hackensack, N.J., : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Homological algebra [[electronic resource] ] : the interplay of homology with distributive lattices and orthodox semigroups / / Marco Grandis
| Homological algebra [[electronic resource] ] : the interplay of homology with distributive lattices and orthodox semigroups / / Marco Grandis |
| Autore | Grandis Marco |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, 2012 |
| Descrizione fisica | 1 online resource (382 p.) |
| Disciplina | 512/.55 |
| Soggetto topico | Algebra, Homological |
| ISBN |
1-281-60370-8
9786613784391 981-4407-07-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; Introduction; 0.1 Homological algebra in a non-abelian setting; 0.2 The coherence problem for subquotients; 0.3 The transfer functor; 0.4 Distributivity and coherence; 0.5 Universal models and crossword chasing; 0.6 Outline; 0.7 Further extensions; 0.8 Literature and terminology; 0.9 Acknowledgements; 1 Coherence and models in homological algebra; 1.1 Some basic notions; 1.1.1 Monomorphisms and epimorphisms; 1.1.2 Lattices; 1.1.3 Distributive and modular lattices; 1.2 Coherence and distributive lattices; 1.2.1 Subquotients and regular induction
1.2.2 Relations of abelian groups1.2.3 Induced relations and canonical isomorphisms; 1.2.4 Examples of incoherence; 1.2.5 Coherent systems of isomorphisms; 1.2.6 Lemma; 1.2.7 Coherence Theorem of homological algebra (Reduced form); 1.3 Coherence and crossword diagrams; 1.3.1 Representing a bifiltered object; 1.3.2 Extending the representation; 1.3.3 Preparing a further extension; 1.3.4 The complete representation; 1.3.5 The Jordan-Holder Theorem; 1.3.6 Representing a sequence of morphisms; 1.4 Coherence and representations of spectral sequences 1.4.1 The universal model of the filtered complex1.4.2 The spectral sequence; 1.4.3 The spectral sequence, continued; 1.4.4 Transgressions; 1.4.5 A non-distributive structure; 1.5 Introducing p-exact categories; 1.5.1 Some terminology; 1.5.2 Pointed categories; 1.5.3 Kernels and cokernels; 1.5.4 Exact categories and exact functors; 1.5.5 Smallness; 1.5.6 Examples; 1.5.7 Galois connections; 1.5.8 Modular lattices and modular connections; 1.6 A synopsis of the projective approach; 1.6.1 Direct and inverse images of abelian groups; 1.6.2 The transfer functor; 1.6.3 Distributivity and coherence 1.6.4 The category of sets and partial bijections1.6.5 Generalisations; 1.7 Free modular lattices; 1.7.1 The Birkhoff Theorem (finite case); 1.7.2 The Birkhoff Theorem (general case); 2 Puppe-exact categories; 2.1 Abelian and p-exact categories; 2.1.1 Additive categories and biproducts; 2.1.2 Lemma (Biproducts); 2.1.3 Theorem and Definition (Semiadditive categories); 2.1.4 Additive categories; 2.1.5 Theorem and definition (Abelian categories); 2.1.6 Biproducts in abelian categories; 2.1.7 Split products in p-exact categories; 2.1.8 Examples of split products 2.1.9 Split products and abelian-valued functors2.2 Subobjects, quotients and the transfer functor; 2.2.1 Kernel duality; 2.2.2 Exact sequences; 2.2.3 Theorem (Modular lattices); 2.2.4 Lemma (Pullbacks and pushouts in p-exact categories); 2.2.5 Direct and inverse images; 2.2.6 Theorem and Definition (The transfer functor); 2.2.7 Subquotients; 2.2.8 Further remarks on modular lattices; 2.2.9 Lemma (Noether isomorphisms); 2.3 Projective p-exact categories and projective spaces; 2.3.1 The associated projective category; 2.3.2 Proposition (The projective congruence of vector spaces) 2.3.3 Projective spaces and projective maps |
| Record Nr. | UNINA-9910790319103321 |
|
Grandis Marco
|
||
| Hackensack, N.J., : World Scientific, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||