Let T be a right exact functor from an abelian category ℬ into another abelian category A.
Then there exists a functor p from the product category A× ℬ to the comma category ((T↓ …

Abstract Let (C, E, s)(C, E, s) be an extriangulated category with a proper class ξ ξ of E E-
triangles. In a previous work, we introduced and studied the ξ ξ-GG projective and the ξ ξ-GG …

This manuscript was written for the Proceedings of the ICRA 2022 in Buenos Aires. It can be
divided into four parts: The first part is an introduction to the theory of monomorphism …

Let (C, E, s) be an extriangulated category with a proper class ξ of E-triangles. We study
complete cohomology of objects in (C, E, s) by applying ξ-projective resolutions and ξ …

Abstract Let R⋉ M be a trivial extension of a ring R by an RR-bimodule M. We first give some
homological formulas over R⋉ M. Then we investigate how to construct (hereditary …

In this paper, we study the cotorsion dimensions and cotorsion triples in the recollements of
abelian categories. The main results are that recollements induce new (resp. complete …

本文研究了形式三角矩阵环上的余挠三元组的问题. 设是形式三角矩阵环, 其中A 和B 是环, U
是左B-右A-双模. 本文利用A-模上完备(完全) 遗传的余挠三元组(C 1, C 2, C 3) 和B …

Let A be a complete and cocomplete abelian category with the additional assumption that
any direct sum and product of short exact sequences are exact. We explore the relation …

Let G (X) and G (Y) be Gorenstein subcategories induced by an admissible balanced pair
(X, Y) in an abelian category A. In this paper, we establish Gorenstein homological …

Let X be an admissible contravariantly finite subcategory of an abelian category A. We show
that A has finite global X-resolution dimension if and only if there is a lower recollement of …