Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product
The injective stabilization of the tensor product is subjected to an iterative procedure that utilizes its bifunctor property. The limit of this procedure, called the asymptotic stabilization of the tensor product, provides a homological counterpart of Buchweitz’s asymptotic construction of stable c...
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| Дата: | 2021 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2021
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188681 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product / A. Martsinkovsky, J. Russell // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 120–151. — Бібліогр.: 17 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1886812023-03-12T01:29:01Z Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product Martsinkovsky, A. Russell, J. The injective stabilization of the tensor product is subjected to an iterative procedure that utilizes its bifunctor property. The limit of this procedure, called the asymptotic stabilization of the tensor product, provides a homological counterpart of Buchweitz’s asymptotic construction of stable cohomology. The resulting connected sequence of functors is isomorphic to Triulzi’s J-completion of the Tor functor. A comparison map from Vogel homology to the asymptotic stabilization of the tensor product is constructed and shown to be always epic. The category of finitely presented functors is shown to be complete and cocomplete. As a consequence, the inert injective stabilization of the tensor product with fixed variable a finitely generated module over an artin algebra is shown to be finitely presented. Its defect and consequently all right-derived functors are determined. New notions of asymptotic torsion and cotorsion are introduced and are related to each other. 2021 Article Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product / A. Martsinkovsky, J. Russell // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 120–151. — Бібліогр.: 17 назв. — англ. 1726-3255 DOI:10.12958/adm1728 2020 MSC: Primary 16E30. http://dspace.nbuv.gov.ua/handle/123456789/188681 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The injective stabilization of the tensor product is subjected to an iterative procedure that utilizes its bifunctor property. The limit of this procedure, called the asymptotic stabilization of the tensor product, provides a homological counterpart of Buchweitz’s asymptotic construction of stable cohomology. The resulting connected sequence of functors is isomorphic to Triulzi’s J-completion of the Tor functor. A comparison map from Vogel homology to the asymptotic stabilization of the tensor product is constructed and shown to be always epic. The category of finitely presented functors is shown to be complete and cocomplete. As a consequence, the inert injective stabilization of the tensor product with fixed variable a finitely generated module over an artin algebra is shown to be finitely presented. Its defect and consequently all right-derived functors are determined. New notions of asymptotic torsion and cotorsion are introduced and are related to each other. |
| format |
Article |
| author |
Martsinkovsky, A. Russell, J. |
| spellingShingle |
Martsinkovsky, A. Russell, J. Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product Algebra and Discrete Mathematics |
| author_facet |
Martsinkovsky, A. Russell, J. |
| author_sort |
Martsinkovsky, A. |
| title |
Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product |
| title_short |
Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product |
| title_full |
Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product |
| title_fullStr |
Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product |
| title_full_unstemmed |
Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product |
| title_sort |
injective stabilization of additive functors, iii. asymptotic stabilization of the tensor product |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2021 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188681 |
| citation_txt |
Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product / A. Martsinkovsky, J. Russell // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 120–151. — Бібліогр.: 17 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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2023-10-18T23:08:54Z |
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