Balanced pairs and recollements in extriangulated categories with negative first extensions

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 balanced pairs and proper classes ξ with enough ξ-projectives and enough ξ-injectives. It can be regarded as a simultaneous generalization of Fu-Hu-Zhang-Zhu and Wang-LiHuang. Besides, we show that if (A,B, C) is a recollement of extriangulated categories, then balanced pairs in B can induce balanced pairs in A and C under natural assumptions. As a application, this result gengralizes a result by Fu-Hu-Yao in abelian categories. Moreover, it highlights a new phenomena when it applied to triangulated categories.

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