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Let (C,E,s) be an extriangulated category with a proper class ξ of E-triangles. In this paper, we study Gorenstein derived functors for extriangulated categories. More precisely, we first introduce the notion of the proper ξ‐Gprojective resolution for an object in C and define the functors ξxtGP(ξ) and ξxtGI(ξ). Under some assumptions, we give some equivalent characterizations for ξ‐Gprojective and ξ‐Ginjective dimensions of objects in C by vanishing of such functors. As an application, our main results generalize Ren and Liu's work. Moreover, our proof is not far from the usual module categories or triangulated categories.
Zhenggang He (Sat,) studied this question.