A Note on the Localization of Pretriangulated Categories

Abstract

For a localizing class \( \mathcal{S} \) of morphisms in a pretriangulated category \( \mathcal{D} \), a weak version of a sufficient condition that guarantees the transfer of the structure of a pretriangulated category onto the localization \( \mathcal{D}\left[{\mathcal{S}}^{-1}\right] \) is proposed. Moreover, the weakness of a similar sufficient condition is obtained in the context of triangulated categories.