Extriangulated categories were introduced by Nakaoka and Palu to give a unification of properties in exact extension-closed subcategories triangulated categories. A notion tilting pairs an extriangulated category is this paper. We Bazzoni characterization setting. also obtain Auslander-Reiten correspondence which classifies finite $\mathcal{C}$-tilting for certain self-orthogonal subcategory $\...

Abstract We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without object. Second, study two classes $\tau$ -tilting-finite algebras and give numbers their two-term Finally, explore when -tilting-finiteness implies representation-finiteness obtain several in which a algebra is representation-finite.