Category-theoretical Definition
In category theory, the notion of Frobenius object is an abstract definition of a Frobenius algebra in a category. A Frobenius object in a monoidal category consists of an object A of C together with four morphisms
such that
- is a monoid object in C,
- is a comonoid object in C,
- the diagrams
and
commute (for simplicity the diagrams are given here in the case where the monoidal category C is strict).
More compactly, a Frobenius algebra in C is a so-called Frobenius monoidal functor A:1 → C, where 1 is the category consisting of one object and one arrow.
Read more about this topic: Frobenius Algebra
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