A category of wide subcategories

TL;DR

This paper introduces a new categorical framework for $ au$-tilting finite algebras, focusing on wide subcategories and support $ au$-tilting pairs, to better understand their structure.

Contribution

It defines a category associated with each $ au$-tilting finite algebra, linking wide subcategories and support $ au$-tilting pairs, a novel approach in the study of these algebras.

Findings

Established a categorical structure for $ au$-tilting finite algebras.

Connected wide subcategories with support $ au$-tilting pairs.

Provided new insights into the organization of modules over such algebras.

Abstract

An algebra is said to be \emph{$\tau$-tilting finite} provided it has only a finite number of $\tau$-rigid objects up to isomorphism. We associate a category to each such algebra. The objects are the wide subcategories of its category of finite dimensional modules, and the morphisms are indexed by support $\tau$-tilting pairs.