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تسجيل مستخدم جديدBalanced pairs and recollements in extriangulated categories with negative first extensions
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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 $xi$ with enough $xi$-projectives and enough $xi$-injectives. It can be regarded as a simultaneous generalization of Fu-Hu-Zhang-Zhu and Wang-Li-Huang. Besides, we show that if $(mathcal A ,mathcal B,mathcal C)$ is a recollement of extriangulated categories, then balanced pairs in $mathcal B$ can induce balanced pairs in $mathcal A$ and $mathcal C$ 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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