Let A be a finite-dimensional algebra, and M be a d-cluster tilting subcategory of mod A.
From the viewpoint of higher homological algebra, a natural question to ask is when M …

Let T be a triangulated category. If T is a cluster tilting object and I=[add T] is the ideal of
morphisms factoring through an object of add T, then the quotient category T/I is abelian …

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We introduce the concept of a pseudo-cluster-tilting subcategory from the viewpoint of the
fact that the quotient of an exact category by a cluster-tilting subcategory is an abelian …

Let $\mathcal {A} $ be a small dg category over a field $ k $ and let $\mathcal {U} $ be a
small full subcategory of the derived category $\mathcal {D}\mathcal {A} $ which generates …

In this paper, we consider a kind of ideal quotient of an extriangulated category such that the
ideal is the kernel of a functor from this extriangulated category to an abelian category. We …

Let $\Phi $ be a finite dimensional $ K $-algebra and let $\mathscr {C}=\textrm {mod}\:\Phi $
be the abelian category of finitely generated right $\Phi $-modules. In their 1985 …

Let $\mathcal C $ be a Krull-Schmidt triangulated category with shift functor $[1] $ and
$\mathcal R $ be a rigid subcategory of $\mathcal C $. We are concerned with the mutation …

Let $ U $ be a silting object in a derived category over a dg-algebra $ A $, and let $ B $ be
the endomorphism dg-algebra of $ U $. Under some appropriate hypotheses, we show that …

From the viewpoint of higher homological algebra, we introduce pure semisimple n-abelian
categories, which are analogs of pure semisimple abelian categories. Let Λ be an Artin …