τ-PERPENDICULAR WIDE SUBCATEGORIES

Let Lambda be a finite-dimensional algebra. A wide subcategory of mod Lambda is called left finite if the smallest torsion class containing it is functorially finite. In this article, we prove that the wide subcategories of mod Lambda arising from tau-tilting reduction are precisely the Serre subcategories of left-finite wide subcategories. As a consequence, we show that the class of such subcategories is closed under further tau-tilting reduction. This leads to a natural way to extend the definition of the "tau-cluster morphism category" of Lambda to arbitrary finite-dimensional algebras. This category was recently constructed by Buan-Marsh in the tau-tilting finite case and by Igusa-Todorov in the hereditary case.