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

TL;DR

This paper explores how certain tilting subcategories in abelian categories relate within recollements, establishing conditions for their transfer and application to tau-cotorsion torsion triples.

Contribution

It demonstrates that Wakamatsu tilting and weak support tau-tilting subcategories can be transferred across recollement structures in abelian categories, with natural assumptions for the converse.

Findings

Wakamatsu tilting subcategories in A and C induce such subcategories in B.

Weak support tau-tilting subcategories in A and C induce similar subcategories in B.

Applications to tau-cotorsion torsion triples in the context of 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).