Frobenius category

In category theory, a branch of mathematics, a Frobenius category is an exact category with enough projectives and enough injectives, where the classes of projectives and injectives coincide. It is an analog of a Frobenius algebra.

Properties

The stable category of a Frobenius category is canonically a triangulated category.[1]

gollark: So Debian is nonfree because it says you can add a repository for nonfree stuff?
gollark: I've said it before, you know.
gollark: PotatOS was literally made because of Terrariola.
gollark: Well, deploying orbital laser strike on terra I guess.
gollark: Really, Terra? If it *allows* you to install nonfree stuff it's beehiveful?

See also

References
  1. Theorem 2.6 in Happel, Dieter (1988). Triangulated Categories in the Representation Theory of Finite Dimensional Algebras. Cambridge University Press. ISBN 9780511629228.
  • Frobenius category in nLab
  • Section 13.4 of Bühler, Theo (2010). "Exact Categories". Expositiones Mathematicae. 28 (1): 1–69.


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