As shown by Happel, from any Frobenius exact category, we can construct a triangulated category as a stable category. On the other hand, it was shown by Iyama and Yoshino that if a pair of subcategories $\mathcal{ D}\subseteq\mathcal{ Z}$ in a triangulated category satisfies certain conditions (i.e., $(\mathcal{ Z},\mathcal{ Z})$ is a $\mathcal{ D}$-mutation pair), then $\mathcal{ Z}/\mathcal{ D}$ becomes a triangulated category. In this article, we consider a simultaneous generalization of these two constructions.
Categories: math.CT