Lifting to cluster-tilting objects in higher cluster categories (Q2859258)

In the paper under review it is shown that if \({\mathcal{C}}\) is a \(d+1\)-Calabi-Yau category with a \(d\)-cluster tilting object \(T\) (where \(d>1\) is an integer) and \(\Gamma=\mathrm{End}_{\mathcal{C}}(T)\) is the endomorphism ring of \(T\), then every tilting \(\Gamma\)-module \(L\) lifts to a \(d\)-cluster tilting object of \({\mathcal{C}}\). The sense of the lifting is the following: The contravariant Hom functor \(\mathrm{Hom}_{\mathcal{C}}(T,-)\) induces an equivalence between an appropriate quotient category and the category of finitely generated \(\Gamma\)-modules; \(L\) lifts to a \(d\)-cluster tilting object if there is such an object which is sent to \(L\) by the composition between \(\mathrm{Hom}_{\mathcal{C}}(T,-)\) and the quotient functor.