nLab Frobenius category

Contents

under construction

Context

Additive and abelian categories

Homological algebra

homological algebra

(also nonabelian homological algebra)

Introduction

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Contents

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 TT is triangle equivalent to the stable category of a Frobenius category, then we say that TT is algebraic.

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

References

In view of Deligne's theorem on tensor categories:

Last revised on June 14, 2022 at 04:05:05. See the history of this page for a list of all contributions to it.