Wakamatsu tilting subcategories and weak support tau-tilting subcategories in recollement

In this article, we prove that if (A, B, C) is a recollement of abelian categories, then wakamatsu tilting (resp. weak support tau-tilting) subcategories in A and C can induce wakamatsu tilting (resp. weak support tau-tilting) subcategories in B, and the converses hold under natural assumptions. As...

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Bibliographic Details
Main Authors Wang, Yongduo, Luo, Hongyang, He, Jian, Wu, Dejun
Format Journal Article
LanguageEnglish
Published 11.09.2024
Subjects
Mathematics - Category Theory
Mathematics - K-Theory and Homology
Mathematics - Representation Theory
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Summary:In this article, we prove that if (A, B, C) is a recollement of abelian categories, then wakamatsu tilting (resp. weak support tau-tilting) subcategories in A and C can induce wakamatsu tilting (resp. weak support tau-tilting) subcategories in B, and the converses hold under natural assumptions. As an application, we mainly consider the relationship of tau-cotorsion torsion triples in (A, B, C).
DOI:10.48550/arxiv.2409.07026