Abstract Let (C, E, s)(C, E, s) be an extriangulated category with a proper class ξ ξ of E E-
triangles. In a previous work, we introduced and studied the ξ ξ-GG projective and the ξ ξ-GG …

Let C be a triangulated category. We first introduce the notion of balanced pairs in C, and
then establish the bijective correspondence between balanced pairs and proper classes ξ …

Abstract Let\({\cal C}=({\cal C},\mathbb {E},\mathfrak {s})\) be an extriangulated category. In
this paper, we give the notion of ideal balanced pairs in\({\cal C}\) and some equivalent …

Let (C, E, s) be an extriangulated category with a proper class ξ of E-triangles. We study
complete cohomology of objects in (C, E, s) by applying ξ-projective resolutions and ξ …

A notion of balanced pairs in an extriangulated category with a negative first extension is
defined in this article. We prove that there exists a bijective correspondence between …

We introduce and study the relative left derived functor Tor n (F, F′)(−,−) in the module
category, which unifies several related left derived functors. Then we give some criteria for …