Resolving resolution dimensions in triangulated categories-Reference-Cited by-同舟云学术

Resolving resolution dimensions in triangulated categories

Published:2021-01-01 Issue:1 Volume:19 Page:121-143
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Ma Xin¹,Zhao Tiwei²

Affiliation:

1. College of Science, Henan University of Engineering , Zhengzhou 451191 , China

2. School of Mathematical Sciences, Qufu Normal University , Qufu 273165 , China

Abstract

Abstract Let

{\mathcal{T}}

be a triangulated category with a proper class

\xi

of triangles and

{\mathcal{X}}

be a subcategory of

{\mathcal{T}}

. We first introduce the notion of

{\mathcal{X}}

-resolution dimensions for a resolving subcategory of

{\mathcal{T}}

and then give some descriptions of objects having finite

{\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

{\mathcal{X}}

-resolution dimensions in terms of a notion of

\xi

-cellular towers. We also construct a new resolving subcategory from a given resolving subcategory and reformulate some known results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2021-0013/pdf

Reference19 articles.

1. M. Auslander and M. Bridger , Stable Module Theory, American Mathematical Society, Providence, 1969.

2. M. Auslander and I. Reiten , Applications of contravariantly finite subcategories, Adv. Math. 86 (1991), no. 1, 111–152, https://doi.org/10.1016/0001-8708(91)90037-8 .

3. V. Becerril , O. Mendoza , M. A. Pérez , and V. Santiago , Frobenius pairs in abelian categories, J. Homotopy Relat. Struct. 14 (2019), 1–50, https://doi.org/10.1007/s40062-018-0208-4 .

4. M. Auslander and R. O. Buchweitz , The homological theory of maximal Cohen-Macaulay approximations, Mem. Soc. Math. France 38 (1989), 5–37, https://doi.org/10.24033/msmf.339 .

5. O. M. Hernández , E. C. S. Valadez , V. S. Vargas , and M. J. S. Salorio , Auslander-Buchweitz approximation theory for triangulated categories, Appl. Categ. Struct. 21 (2013), 119–139, https://doi.org/10.1007/s10485-011-9261-4 .

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