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.