Intermediate co-t-structures, two-term silting objects, tau-tilting modules, and torsion classes

Abstract

If (A,B) and (A',B') are co-t-structures of a triangulated category, then (A',B') is called intermediate if A \subseteq A' \subseteq \Sigma A. Our main results show that intermediate co-t-structures are in bijection with two-term silting subcategories, and also with support tau-tilting subcategories under some assumptions. We also show that support tau-tilting subcategories are in bijection with certain finitely generated torsion classes. These generalise results by Adachi, Iyama, and Reiten.