From triangulated categories to module categories via localisation (Q2838107)

The authors proved that for a rigid object \(T\) in a triangulated Hom-finite Krull-Schmidt category \(\mathcal{C}\), the Gabriel-Zisman localization of \(\mathcal{C}\) is equivalent to the finite dimensional module category of \(\text{End}_\mathcal{C}(T)^{op}\). This generalizes a 2-Calabi-Yau Tilting Theorem in [\textit{B. Keller} and \textit{I. Reiten}, Adv. Math. 211, No. 1, 123--151 (2007; Zbl 1128.18007)], which says \(\mathcal{C}/\Sigma T\) is equivalent to such a module category, provided further conditions that \(T\) is cluster-tilting and \(\mathcal{C}\) is 2-Calabi-Yau.