Non-Abelian Homological Algebra and Its Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
421 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | While in classical (abelian) homological algebra additive functors from abelian (or additive) categories to abelian categories are investigated , non- abelian homological algebra deals with non-additive functors and their homological properties , in particular with functors having values in non-abelian categories. Such functors haveimportant applications in algebra, algebraic topology, functional analysis, algebraic geometry and other principal areas of mathematics. To study homological properties of non-additive functors it is necessary to define and investigate their derived functors and satellites. It will be the aim of this book based on the results of researchers of A. Razmadze Mathematical Institute of the Georgian Academy of Sciences devoted to non-abelian homological algebra. The most important considered cases will be functors from arbitrary categories to the category of modules, group valued functors and commutative semigroup valued functors. In Chapter I universal sequences of functors are defined and in vestigated with respect to (co)presheaves of categories, extending in a natural way the satellites of additive functors to the non-additive case and generalizing the classical relative homological algebra in additive categories to arbitrary categories. Applications are given in the furth coming chapters. Chapter II is devoted to the non-abelian derived functors of group valued functors with respect to projective classes using projective pseu dosimplicial resolutions. Their functorial properties (exactness, Milnor exact sequence, relationship with cotriple derived functors, satellites and Grothendieck cohomology, spectral sequence of an epimorphism, degree of an arbitrary functor) are established and applications to ho mology and cohomology of groups are given |
| Beschreibung: | 1 Online-Ressource (V, 266 p) |
| ISBN: | 9789401588539 9789048148998 |
| DOI: | 10.1007/978-94-015-8853-9 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
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| institution | BVB |
| isbn | 9789401588539 9789048148998 |
| language | English |
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| spelling | Inassaridze, Hvedri Verfasser aut Non-Abelian Homological Algebra and Its Applications by Hvedri Inassaridze Dordrecht Springer Netherlands 1997 1 Online-Ressource (V, 266 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 421 While in classical (abelian) homological algebra additive functors from abelian (or additive) categories to abelian categories are investigated , non- abelian homological algebra deals with non-additive functors and their homological properties , in particular with functors having values in non-abelian categories. Such functors haveimportant applications in algebra, algebraic topology, functional analysis, algebraic geometry and other principal areas of mathematics. To study homological properties of non-additive functors it is necessary to define and investigate their derived functors and satellites. It will be the aim of this book based on the results of researchers of A. Razmadze Mathematical Institute of the Georgian Academy of Sciences devoted to non-abelian homological algebra. The most important considered cases will be functors from arbitrary categories to the category of modules, group valued functors and commutative semigroup valued functors. In Chapter I universal sequences of functors are defined and in vestigated with respect to (co)presheaves of categories, extending in a natural way the satellites of additive functors to the non-additive case and generalizing the classical relative homological algebra in additive categories to arbitrary categories. Applications are given in the furth coming chapters. Chapter II is devoted to the non-abelian derived functors of group valued functors with respect to projective classes using projective pseu dosimplicial resolutions. Their functorial properties (exactness, Milnor exact sequence, relationship with cotriple derived functors, satellites and Grothendieck cohomology, spectral sequence of an epimorphism, degree of an arbitrary functor) are established and applications to ho mology and cohomology of groups are given Mathematics Geometry, algebraic Algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Associative Rings and Algebras Algebraic Topology Algebraic Geometry Mathematik Nichtabelsche Gruppe (DE-588)4340007-3 gnd rswk-swf Homologische Algebra (DE-588)4160598-6 gnd rswk-swf Nichtabelsche Gruppe (DE-588)4340007-3 s Homologische Algebra (DE-588)4160598-6 s 1\p DE-604 https://doi.org/10.1007/978-94-015-8853-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Inassaridze, Hvedri Non-Abelian Homological Algebra and Its Applications Mathematics Geometry, algebraic Algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Associative Rings and Algebras Algebraic Topology Algebraic Geometry Mathematik Nichtabelsche Gruppe (DE-588)4340007-3 gnd Homologische Algebra (DE-588)4160598-6 gnd |
| subject_GND | (DE-588)4340007-3 (DE-588)4160598-6 |
| title | Non-Abelian Homological Algebra and Its Applications |
| title_auth | Non-Abelian Homological Algebra and Its Applications |
| title_exact_search | Non-Abelian Homological Algebra and Its Applications |
| title_full | Non-Abelian Homological Algebra and Its Applications by Hvedri Inassaridze |
| title_fullStr | Non-Abelian Homological Algebra and Its Applications by Hvedri Inassaridze |
| title_full_unstemmed | Non-Abelian Homological Algebra and Its Applications by Hvedri Inassaridze |
| title_short | Non-Abelian Homological Algebra and Its Applications |
| title_sort | non abelian homological algebra and its applications |
| topic | Mathematics Geometry, algebraic Algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Associative Rings and Algebras Algebraic Topology Algebraic Geometry Mathematik Nichtabelsche Gruppe (DE-588)4340007-3 gnd Homologische Algebra (DE-588)4160598-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Associative Rings and Algebras Algebraic Topology Algebraic Geometry Mathematik Nichtabelsche Gruppe Homologische Algebra |
| url | https://doi.org/10.1007/978-94-015-8853-9 |
| work_keys_str_mv | AT inassaridzehvedri nonabelianhomologicalalgebraanditsapplications |