Abelian model structures on comma categories
UDC 512.64 Let $\mathsf{A}$ and $\mathsf{B}$ be bicomplete Abelian categories, which both have enough projectives and injectives and let $T\colon\mathsf{A}\rightarrow\mathsf{B}$ be a right exact functor. Under some mild conditions, we show that hereditary Abelian model structures on $\m...
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| Date: | 2024 |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7289 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512644691132416 |
|---|---|
| author | Tang, Guoliang Tang, Guoliang |
| author_facet | Tang, Guoliang Tang, Guoliang |
| author_sort | Tang, Guoliang |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:15Z |
| description | UDC 512.64
Let $\mathsf{A}$ and $\mathsf{B}$ be bicomplete Abelian categories, which both have enough projectives and injectives and let $T\colon\mathsf{A}\rightarrow\mathsf{B}$ be a right exact functor. Under some mild conditions, we show that hereditary Abelian model structures on $\mathsf{A}$ and $\mathsf{B}$ can be amalgamated into a global hereditary Abelian model structure on the comma category  $(T\downarrow\mathsf{B})$. As an application of this result, we give an explicit description of a subcategory that consists of all trivial objects of the Gorenstein flat model structure on the category of modules over a triangular matrix ring. |
| doi_str_mv | 10.3842/umzh.v76i3.7289 |
| first_indexed | 2026-03-24T03:32:04Z |
| format | Article |
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| id | umjimathkievua-article-7289 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:04Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-72892024-06-19T00:35:15Z Abelian model structures on comma categories Abelian model structures on comma categories Tang, Guoliang Tang, Guoliang Abelian model structures; Comma categories; Triangular matrix rings. 18G25; 16G20. UDC 512.64 Let $\mathsf{A}$ and $\mathsf{B}$ be bicomplete Abelian categories, which both have enough projectives and injectives and let $T\colon\mathsf{A}\rightarrow\mathsf{B}$ be a right exact functor. Under some mild conditions, we show that hereditary Abelian model structures on $\mathsf{A}$ and $\mathsf{B}$ can be amalgamated into a global hereditary Abelian model structure on the comma category  $(T\downarrow\mathsf{B})$. As an application of this result, we give an explicit description of a subcategory that consists of all trivial objects of the Gorenstein flat model structure on the category of modules over a triangular matrix ring. УДК 512.64 Абелеві модельні структури на категоріях коми Нехай $\mathsf{A}$ і $\mathsf{B}$ – біповні абелеві категорії, які мають достатню кількість проєктивних та ін'єктивних об'єктів. Крім того, нехай $T\colon\mathsf{A}\rightarrow\mathsf{B}$ – точний правий  функтор. За деяких м'яких умов показано, що спадкові абелеві модельні структури на $\mathsf{A}$ і $\mathsf{B}$ можна об'єднати в глобальну спадкову абелеву модельну структуру на категорії коми  $(T\downarrow\mathsf{B})$. Як застосування цього результату, наведено чіткий опис підкатегорії, що складається з усіх тривіальних об'єктів структури плоскої моделі Горенштейна на категорії модулів над трикутним матричним кільцем. Institute of Mathematics, NAS of Ukraine 2024-03-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7289 10.3842/umzh.v76i3.7289 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 3 (2024); 373 - 381 Український математичний журнал; Том 76 № 3 (2024); 373 - 381 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7289/9854 Copyright (c) 2024 guoliang tang |
| spellingShingle | Tang, Guoliang Tang, Guoliang Abelian model structures on comma categories |
| title | Abelian model structures on comma categories |
| title_alt | Abelian model structures on comma categories |
| title_full | Abelian model structures on comma categories |
| title_fullStr | Abelian model structures on comma categories |
| title_full_unstemmed | Abelian model structures on comma categories |
| title_short | Abelian model structures on comma categories |
| title_sort | abelian model structures on comma categories |
| topic_facet | Abelian model structures Comma categories Triangular matrix rings. 18G25 16G20. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7289 |
| work_keys_str_mv | AT tangguoliang abelianmodelstructuresoncommacategories AT tangguoliang abelianmodelstructuresoncommacategories |