Abstract Let (C, E, s C, E, s) be an extriangulated category with a proper class ξ of E E-
triangles, and WW an additive full subcategory of (C, E, s C, E, s). We provide a method for …

We fix a proper class of 𝔼-triangles ξ in an extriangulated category 𝒞. Let 𝒲 be a class of
objects in 𝒞 such that ξ xt ξ i (W, W′)= 0, ξ xt ξ 0 (−, W)≅ 𝒞 (−, W) and ξ xt ξ 0 (W,−)≅ 𝒞 (W,−) …

This paper mainly studies the relative Gorenstein objects in the extriangulated category
$\mathcal {C}=(\mathcal {C},\mathbb {E},\mathfrak {s}) $ with a proper class $\xi $ and the …