Definition Coinflip in a Markov category [efr-0XH9]

Let \mathcal {C} be a Markov category with finite coproducts. A coinflip in \mathcal {C} is a morphism f: I \to I + I obeying the following equations:

1. Symmetry: \tau _{I,I} f = f, where \tau _{A,B} :A + B \to B + A is the canonical isomorphism.
2. Interchange: (f + f)f = (I + \tau _{I,I} + I)(f + f)f

Given a coinflip in a distributive Markov category, there is a canonical induced natural transformation A \otimes A \to A, which makes every A \in \mathcal {C} into a midpoint algebra.