Frobenius Objects

Frobenius Object

A Frobenius object in a monoidal category is an object equipped with four morphisms

such that is a monoid object, is a comonoid object, and the Frobenius relation holds:

e.g. A Frobenius object in is precisely a Frobenius algebra.

Frobenius Homomorphism

A Frobenius homomorphism between two Frobenius objects and is a morphism that is both a monoid homomorphism and a comonoid homomorphism.
Thus the Frobenius objects together with Frobenius homomorphisms form a category, denoted by .

The Universal Frobenius Structure