Balanced pairs and recollements in extriangulated categories with negative first extensions

Abstract

A notion of balanced pairs in an extriangulated category with a negative first extension is defined in this paper. We prove that there exists a bijective correspondence between balanced pairs and proper classes [Formula: see text] with enough [Formula: see text]-projectives and enough [Formula: see text]-injectives. This can be regarded as a simultaneous generalization of corresponding results of Fu–Hu–Zhang–Zhu for triangulated categories and of Wand–Li-Huang for abelian categories. Besides, we show that if [Formula: see text] is a recollement of extriangulated categories, then balanced pairs in [Formula: see text] can induce balanced pairs in [Formula: see text] and [Formula: see text] under natural assumptions. As an application, this result generalizes a result by Fu–Hu–Yao in abelian categories. Moreover, it highlights a new phenomena when it is applied to triangulated categories.