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

Abstract

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).

arXiv commentAdded Section 6: Examples, to appeaer in Comm. Algebra