Mutation of representations and nearly Morita equivalence

Abstract

Buan-Iyama-Reiten-Smith proved, based on Derksen-Weyman-Zelevinsky work, that the Jacobian algebra of two quivers with potential related by a QP-mutation are nearly Morita equivalent. They proved, using Axiom of Choice, that the natural functor ${\mu }_k$ is an equivalence by showing that ${\mu }_k$ is full, faithfull and dense. In this note we provide a quasi-inverse ${\mu }_k^{-}$ to ${\mu }_k$ without Axiom of Choice.

10 pages