Let $\mathcal {A} $ be an abelian length category containing a $ d $-cluster tilting
subcategory $\mathcal {M} $. We prove that a subcategory of $\mathcal {M} $ is a $ d …

For a higher Nakayama algebra $ A $ in the sense of Jasso-K\"{u} lshammer, we show that
the singularity category of $ A $ is triangulated equivalent to the stable module category of a …

In this short note we construct two families of examples of large stratifying systems in module
categories of algebras. The first examples consist on stratifying systems of infinite size in the …

We introduce the category of finite strings and study its basic properties. The category is
closely related to the augmented simplex category, and it models categories of linear …

Xiao and Zhu proved that if C is a locally finite triangulated category, then C has Auslander–
Reiten triangles. Let n be a positive integer. The notion of n-abelian categories is a higher …

Let k be a commutative artinian ring and 𝒜 a small Ext-finite Krull–Schmidt n-abelian k-
category with enough projectives and injectives. We introduce two full subcategories 𝒜 r and …

We prove that the bounded derived category of the lattice of order ideals of the product of
two ordered chains is fractionally Calabi-Yau. We also show that these lattices are derived …

Let $\Lambda $ be an $ n $-Auslander algebra with global dimension $ n+ 1$. In this paper,
we prove that $\Lambda $ is representation-finite if and only if the number of non-isomorphic …

$ n\mathbb {Z} $-cluster tilting subcategories are an ideal setting for higher dimensional
Auslander-Reiten theory. We give a complete classification of $ n\mathbb {Z} $-cluster tilting …

In this paper, the notion of cotorsion classes is introduced into the higher homological
algebra. Our results motivate the definition, showing that this notion of n-cotorsion classes …