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
References
References
- Theorem 2.6 in Happel, Dieter (1988). Triangulated Categories in the Representation Theory of Finite Dimensional Algebras. Cambridge University Press. ISBN 9780511629228.
- Frobenius category at the nLab
- Section 13.4 of Bühler, Theo (2010). "Exact Categories". Expositiones Mathematicae. 28 (1): 1–69. arXiv:0811.1480. CiteSeerX 10.1.1.758.2107. doi:10.1016/j.exmath.2009.04.004.