Localization of triangulated categories with respect to extension-closed subcategories (Q6587247)

\textit{H. Nakaoka} and \textit{Y. Palu} [Cah. Topol. Géom. Différ. Catég. 60, No. 2, 117--193 (2019; Zbl 1451.18021)] introduced the notion of extriangulated categories. It gives a simultaneous generalization of exact categories and triangulated categories.\N\NLet C be a triangulated category and N an extension-closed subcategory of C. In this paper under review, the authors study the theory of Localization of C with respect to N. More precisely, they construct a natural extriangulated structure on C together with an exact functor Q satisfying a suitable universality. Their construction simultaneously contains the Verdier quotient and certain types of cohomological functors. The main result unifies several phenomena. Finally, the authors also give many applications.