Let $\Lambda $ be a finite-dimensional algebra. A wide subcategory of $\mathsf
{mod}\Lambda $ is called left finite if the smallest torsion class containing it is functorially …

arXiv:2302.12217v2 [math.RT] 19 Apr 2023 Page 1 arXiv:2302.12217v2 [math.RT] 19 Apr
2023 A GEOMETRIC PERSPECTIVE ON THE τ-CLUSTER MORPHISM CATEGORY SIBYLLE …

We introduce the notions of τ-exceptional and signed τ-exceptional sequences for any finite
dimensional algebra. We prove that for a fixed algebra of rank n, and for any positive integer …

An algebra is said to be-tilting finite provided it has only a finite number of-rigid objects up to
isomorphism. To each such algebra, we associate a category whose objects are the wide …

We generalise $\tau $-cluster morphism categories to non-positive proper dg algebras. The
compatibility of silting reduction with support $\tau $-tilting reduction will be an essential …

Let $\mathcal {C} $ be an extriangulated category and let $\mathcal {R}\subseteq\mathcal
{C} $ be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a …

In this paper the notion of an admissible partition of a simplicial polyhedral fan is introduced
and the category of a partitioned fan is defined as a generalisation of the τ τ‐cluster …

The bricks over preprojective algebras of type A are known to be in bijection with certain
combinatorial objects called “arcs”. In this paper, we show how one can use arcs to compute …

We take a novel lattice-theoretic approach to the $\tau $-cluster morphism category
$\mathfrak {T}(A) $ of a finite-dimensional algebra $ A $ and define the category via the …

Abstract Recently, Buan and Marsh showed that if two complete τ-exceptional sequences
agree in all but at most one term, then they must agree everywhere, provided the algebra is τ …