Frobenius category

A **Frobenius category** is a Quillen exact category which has enough injectives and enough projectives and where the class of projectives coincides with the class of injectives. The stable category of a Frobenius category is canonically a triangulated category. If a triangulated category $T$ is triangle equivalent to the stable category of a Frobenius category, then we say that $T$ is *algebraic*.