We describe a reduction technique for stably 2-Calabi--Yau Frobenius extriangulated
categories $\mathcal {F} $ with respect to a functorially finite rigid subcategory $\mathcal {X} …

We give a simultaneous generalization of recollements of abelian categories and
triangulated categories, which we call recollements of extriangulated categories. For a …

nspired by the work of J $\o $ rgensen [J], we define a (upper-, lower-) symmetric
recollements; and give a one-one correspondence between the equivalent classes of the …

Given an abelian category, we introduce a categorical concept of (strongly) Gorenstein
projective (resp., injective) objects, by defining a new special class of objects. Then we study …

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 $ 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 …

This paper is devoted to constructing some recollements of additive categories associated to
concentric twin cotorsion pairs on an extriangulated category. As an application, this result …

Let (S; n) be a commutative noetherian local ring and let w in n be non-zero divisor. This
paper is concerned with the two categories of monomorphisms between finitely generated …

Let CC be a triangulated category and EE a proper class of triangles. We show that Tate
cohomology in triangulated category is balanced, ie there is an isomorphism E xt ̂ P i (A …

Let A be a finite-dimensional Gorenstein algebra of finite CM-type. We show that the
Gorenstein derived category of A has Auslander–Reiten triangles. In this case, we otain a …