Mutation of representations and nearly Morita equivalence

Diego Fernando, Velasco Martínez

Published 2015-10-20Version 1

In \cite{BIRS} it was proved, based on \cite{DWZI}, 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 an quasi-inverse $\mu_k^-$ to $\mu_k$ without Axiom of Choice.