nLab Frobenius category

under construction

Idea

One definition says (where?) that: 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.

Another (?) definition is given in Etingof & Ostrik 2021, §1.3.

References

• Pavel Etingof, Victor Ostrik, On the Frobenius functor for symmetric tensor categories in positive characteristic, J. für die reine und angewandte Mathematik 773 (2021) 165–198 $[$arXiv:1912.12947$]$

In view of Deligne's theorem on tensor categories:

• Kevin Coulembier, Pavel Etingof, Victor Ostrik, On Frobenius exact symmetric tensor categories $[$arXiv:2107.02372$]$