Universal localizations of d-homological pairs

Let \(k\) be an algebraically closed field and \(A\) a finite dimensional k-algebra. The universal localization of \(A\) with respect to a set of morphisms between finitely generated projective \(A\)-modules always exists. When \(A\) is hereditary, Krause and Stovicek proved that the universal localizations of \(A\) are in bijection with various natural structures.

In this talk I will introduce the higher analogue of universal localizations, that is universal localizations of \(d\)-homological pairs with respect to certain wide subcategories, and show a (partial) generalisation of Krause and Stovicek result in the higher setup.