Let A be an abelian category and P (A) be the subcategory of A consisting of projective
objects. Let C be a full, additive and self-orthogonal subcategory of A with P (A) a generator …

We study a structure of subcategories which are called a polygon of recollements in a
triangulated category. First, we study a $2 n $-gon of recollements in an $(m/n) $-Calabi-Yau …

For any ring R, we show that, in the bounded derived category Db (Mod R) of le R-modules,
the subcategory of complexes with nite Gorenstein projective (resp. injective) dimension …

Let $\mathcal X $ be a subcategory of left $ S $-modules and $ _ {R} U_ {S} $ an $(R, S) $-
bimodule. As a generalization of an adjoint cotranspose, we introduce an adjoint $\mathcal …

For $\Lambda $ a selfinjective algebra, and $ Q $ a finite quiver without oriented cycles, the
algebra $\Lambda Q $ is a Gorenstein algebra and the category ${\rm Gproj}\Lambda Q $ of …

Abstract Let (F′, F, F ″) be a comparison of left recollements of triangulated categories
such that F′ and F ″are equivalences. We prove that if F is full then F is an equivalence; …

We introduce the notion of balanced pair of additive subcategories in an abelian category.
We give sufficient conditions under which a balanced pair of subcategories gives rise to a …

We give a general parametrization of all the recollement data for a triangulated category with
a set of generators. From this we deduce a characterization of when a ℵ0-perfectly …

For a $ k $-algebra $ A $, a quiver $ Q $, and an ideal $ I $ of $ kQ $ generated by monomial
relations, let $\Lambda:= A\otimes_k kQ/I $. We introduce the monic representations of $(Q …

For a finite acyclic quiver Q, an ideal I of a path algebra kQ generated by monomial relations,
and a finite-dimensional k-algebra A, we introduce the separated monic representations of a …