Geodesic
A note on localization of pretriangulated categories
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 67-73 
A. I. Generalov. A note on localization of pretriangulated categories. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 67-73. http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a6/
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     title = {A~note on localization of pretriangulated categories},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For a localising class $\mathcal S$ of morphisms in a pretriangulated category $\mathcal D$, a weak version of a sufficient condition that guarantees carrying the structure of pretriangulated category onto the localisation $\mathcal{D[S}^{-1}]$ is proposed. Moreover, we get a similar weakness of a sufficient condition in the context of triangulated categories.

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