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 sta...
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| Дата: | 2021 |
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| Мова: | English |
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Lugansk National Taras Shevchenko University
2021
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1728 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-17282021-04-11T06:11:31Z Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product Martsinkovsky, A. Russell, J. injective stabilization, asymptotic stabilization, asymptotic torsion, asymptotic cotorsion 16E30 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. Lugansk National Taras Shevchenko University The first author is supported in part by the Shota Rustaveli National Science Foundation of Georgia Grant NFR-18-10849 2021-04-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1728 10.12958/adm1728 Algebra and Discrete Mathematics; Vol 31, No 1 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1728/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1728/789 Copyright (c) 2021 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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|
| datestamp_date |
2021-04-11T06:11:31Z |
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OJS |
| language |
English |
| topic |
injective stabilization asymptotic stabilization asymptotic torsion asymptotic cotorsion 16E30 |
| spellingShingle |
injective stabilization asymptotic stabilization asymptotic torsion asymptotic cotorsion 16E30 Martsinkovsky, A. Russell, J. Injective stabilization of additive functors, III. Asymptotic stabilization of the tensor product |
| topic_facet |
injective stabilization asymptotic stabilization asymptotic torsion asymptotic cotorsion 16E30 |
| format |
Article |
| author |
Martsinkovsky, A. Russell, J. |
| 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 |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1728 |
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AT martsinkovskya injectivestabilizationofadditivefunctorsiiiasymptoticstabilizationofthetensorproduct AT russellj injectivestabilizationofadditivefunctorsiiiasymptoticstabilizationofthetensorproduct |
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2025-07-17T10:36:14Z |
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2025-07-17T10:36:14Z |
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1837890089511813121 |