Additive categories play a fundamental role in mathematics and related disciplines. Given
an additive category equipped with a biadditive functor, one can construct its category of …

We investigate the role of gentle algebras in higher homological algebra. In the first part of
the paper, we show that if the module category of a gentle algebra Λ contains ad-cluster …

We prove the conjecture that the higher Tamari orders of Dimakis and M\" uller-Hoissen
coincide with the first higher Stasheff--Tamari orders. To this end, we show that the higher …

We show that isomorphism classes of indecomposable-rigid pairs over, the preprojective
algebra of, are in bijection with internal-simplices in the prism, the product of an-simplex with …

The set of triangulations of a cyclic polytope possesses two a priori different partial orders,
known as the higher Stasheff–Tamari orders. The first of these orders was introduced by …

Abstract n Z-cluster tilting subcategories are an ideal setting for higher dimensional
Auslander–Reiten theory. We give a complete classification of n Z-cluster tilting …

Motivated by higher homological algebra, we associate quivers to triangulations of even-
dimensional cyclic polytopes and prove two results showing what information about the …

We define a poset called the Outer Tamari poset, and show it is isomorphic to a subposet of
the Tamari lattice introduced by Pallo (1986), and studied further and called the Comb poset …

In this article we study higher homological properties of $ n $-levelled algebras and connect
them to properties of the underlying graphs. Notably, to each $2 $-representation-finite …

We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of
higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their …