under construction
additive and abelian categories
(AB1) pre-abelian category
(AB2) abelian category
(AB5) Grothendieck category
left/right exact functor
(also nonabelian homological algebra)
Context
Basic definitions
Stable homotopy theory notions
Constructions
Lemmas
Homology theories
Theorems
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.
In view of Deligne's theorem on tensor categories:
Last revised on June 14, 2022 at 08:05:05. See the history of this page for a list of all contributions to it.