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 …

Let $(\mathcal {C},\mathbb {E},\mathfrak {s}) $ be an extriangulated category with a proper
class $\xi $ of $\mathbb {E} $-triangles. In this paper, we study Gorenstein derived functors …

Let $\mathcal {C} $ be a triangulated category with a proper class $\xi $ of triangles.
Asadollahi and Salarian introduced and studied $\xi $-Gorenstein projective and $\xi …

We give the definition of Gorenstein syzygy objects in extriangulated categories and obtain a
characterization. For a recollement of extriangulated categories, we mainly show that …

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,−) …

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. A notion of proper class in an …

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 …

Let $ k $ be a commutative ring, let ${\mathcal {C}} $ be a small, $ k $-linear, Hom-finite,
locally bounded category, and let ${\mathcal {B}} $ be a $ k $-linear abelian category. We …

Let C be a triangulated category with a proper class E of triangles. Asadollahi and Salarian
introduced and studied EG projective and EG injective objects, and developed a relative …

In this paper, we introduce and study preresolving subcategories in an extriangulated
category~ $\mathscr {C} $. Let $\mathcal {Y} $ be a $\mathcal {Z} $-preresolving …