Resolving resolution dimensions in triangulated categories

Let T{\mathcal{T}} be a triangulated category with a proper class ξ\xi of triangles and X{\mathcal{X}} be a subcategory of T{\mathcal{T}}. We first introduce the notion of X{\mathcal{X}}-resolution dimensions for a resolving subcategory of T{\mathcal{T}} and then give some descriptions of objects h...

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Autores principales:	Ma Xin, Zhao Tiwei
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	triangulated categories a proper class of triangles resolving resolution dimensions resolving subcategories auslander-buchweitz approximations 18g20 18g25 18g10 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/734d471faeec407e8b816d04385e0357
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id	oai:doaj.org-article:734d471faeec407e8b816d04385e0357
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spelling	oai:doaj.org-article:734d471faeec407e8b816d04385e03572021-12-05T14:10:52ZResolving resolution dimensions in triangulated categories2391-545510.1515/math-2021-0013https://doaj.org/article/734d471faeec407e8b816d04385e03572021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0013https://doaj.org/toc/2391-5455Let T{\mathcal{T}} be a triangulated category with a proper class ξ\xi of triangles and X{\mathcal{X}} be a subcategory of T{\mathcal{T}}. We first introduce the notion of X{\mathcal{X}}-resolution dimensions for a resolving subcategory of T{\mathcal{T}} and then give some descriptions of objects having finite X{\mathcal{X}}-resolution dimensions. In particular, we obtain Auslander-Buchweitz approximations for these objects. As applications, we construct adjoint pairs for two kinds of inclusion functors and characterize objects having finite X{\mathcal{X}}-resolution dimensions in terms of a notion of ξ\xi -cellular towers. We also construct a new resolving subcategory from a given resolving subcategory and reformulate some known results.Ma XinZhao TiweiDe Gruyterarticletriangulated categoriesa proper class of trianglesresolving resolution dimensionsresolving subcategoriesauslander-buchweitz approximations18g2018g2518g10MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 121-143 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	triangulated categories a proper class of triangles resolving resolution dimensions resolving subcategories auslander-buchweitz approximations 18g20 18g25 18g10 Mathematics QA1-939
spellingShingle	triangulated categories a proper class of triangles resolving resolution dimensions resolving subcategories auslander-buchweitz approximations 18g20 18g25 18g10 Mathematics QA1-939 Ma Xin Zhao Tiwei Resolving resolution dimensions in triangulated categories
description	Let T{\mathcal{T}} be a triangulated category with a proper class ξ\xi of triangles and X{\mathcal{X}} be a subcategory of T{\mathcal{T}}. We first introduce the notion of X{\mathcal{X}}-resolution dimensions for a resolving subcategory of T{\mathcal{T}} and then give some descriptions of objects having finite X{\mathcal{X}}-resolution dimensions. In particular, we obtain Auslander-Buchweitz approximations for these objects. As applications, we construct adjoint pairs for two kinds of inclusion functors and characterize objects having finite X{\mathcal{X}}-resolution dimensions in terms of a notion of ξ\xi -cellular towers. We also construct a new resolving subcategory from a given resolving subcategory and reformulate some known results.
format	article
author	Ma Xin Zhao Tiwei
author_facet	Ma Xin Zhao Tiwei
author_sort	Ma Xin
title	Resolving resolution dimensions in triangulated categories
title_short	Resolving resolution dimensions in triangulated categories
title_full	Resolving resolution dimensions in triangulated categories
title_fullStr	Resolving resolution dimensions in triangulated categories
title_full_unstemmed	Resolving resolution dimensions in triangulated categories
title_sort	resolving resolution dimensions in triangulated categories
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/734d471faeec407e8b816d04385e0357
work_keys_str_mv	AT maxin resolvingresolutiondimensionsintriangulatedcategories AT zhaotiwei resolvingresolutiondimensionsintriangulatedcategories
_version_	1718371647490097152

Resolving resolution dimensions in triangulated categories

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