Support Tau n-tilting pairs

We introduce the higher version of Adachi-Iyama-Reiten's support r-tilting pairs, which are regarded as a generalization of maximal rn-rigid pairs in the sense of Jacobsen-Jorgensen. Assume that C is an (n + 2)-angulated category with an n-suspension functor Sigma n and T is an Opperman-Thomas cluster tilting object. We prove that relative n-rigid objects in C are in bijection with rn-rigid pairs in the n-abelian category C/add Sigma nT, and relative maximal n-rigid objects in C are in bijection with support rn-tilting pairs. We also prove that relative n-self-perpendicular objects are in bijection with maximal rn-rigid pairs. These results generalize work for C being 2n-Calabi-Yau by Jacobsen-Jorgensen and work for n = 1 by Yang-Zhu.(c) 2022 Elsevier Inc. All rights reserved.