From triangulated categories to module categories via localisation. II: Calculus of fractions. (Q2909046)

Let \(\mathcal C\) be a skeletally small triangulated Hom-finite Krull-Schmidt \(k\)-category (over a field \(k\)) with Serre duality. \textit{S. Koenig} and \textit{B. Zhu} [Math. Z. 258, No. 1, 143-160 (2008; Zbl 1133.18005)] have shown that for a cluster tilting object \(T\), the factor category \(\mathcal C/[\Sigma T]\) is a category of finitely presented modules over the endomorphism ring of \(T\). The authors extend this result to rigid objects \(T\). They show first that the factor category \(\mathcal C/[T^\perp]\) is integral, that is, the regular morphisms in this category admit a calculus of fractions such that the quotient category is Abelian. The main result states that the quotient category of \(\mathcal C/[T^\perp]\) is equivalent to the category of finitely presented modules over the endomorphism ring of \(T\).NEWLINENEWLINE For part I see the authors [Trans. Am. Math. Soc. 365, No. 6, 2845-2861 (2013; Zbl 1327.18022)].