Let (C, E, s) be an extriangulated category with a proper class ξ of E-triangles and X a
resolving subcategory of C. In this paper, we introduce the notion of X-resolution dimension …

Let T be a triangulated category with a proper class ξ of triangles and X be a subcategory of
T. We first introduce the notion of X-resolution dimensions for a resolving subcategory of T …

We consider the notion of pre-extriangulated categories. We give some characterizations of
almost split $\mathfrak s $-triangles in a pre-extriangulated category and provide necessary …

Let XX be an extension-closed subcategory of a triangulated category such that XX admits a
weak-cogenerator W W. We investigate finite resolutions by objects in XX and X X-resolution …

Let (𝒜, ℬ, 𝒞) be a recollement of extriangulated categories with a negative first extension
and 𝒳 ℬ be a generative subcategory of ℬ. We prove that 𝒜 and 𝒞 have a generative …

In this paper, we mainly focus on extension-closed subcategories of extriangulated
categories. Let X be an extension-closed subcategory. We show that if C is X-projective and …

Let E be a proper class of triangles in a triangulated category C; and let (A, B, C) be a
recollement of triangulated categories. Based on Beligiannis's work, we prove that A and C …

Let (A, B, C) be a recollement of extriangulated categories. In this paper we introduce the
global dimension and extension dimension of extriangulated categories, and give some …

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. In this paper, we introduce …

In this work we study how to extend the concept of\emph {" reduction,"} given for rigid and
functorially finite subcategories in an extriangulated category $\mathcal {C} $, to $(n+ 2) …