Frobenius category explained

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]

See also

• Dagger compact category
• Tannakian category

References

• • Section 13.4 of Bühler . Theo . Exact Categories . Expositiones Mathematicae . 2010 . 28 . 1 . 1–69 . 10.1.1.758.2107 . 0811.1480 . 10.1016/j.exmath.2009.04.004 .

Notes and References

1. Theorem 2.6 in Book: Happel . Dieter . Triangulated Categories in the Representation Theory of Finite Dimensional Algebras . 1988 . Cambridge University Press . 9780511629228.