Corollary [efr-REOY]

Any iterable midpoint algebra carries the structure of an algebra of \bar {\Delta }. Moreover any midpoint homomorphism between iterable midpoint algebras is a \bar {\Delta }-homomorphism. In particular, if \mathcal {C} is an externally iterable coinflip Markov category, each homset \mathcal {C}(X,Y) is a \bar {\Delta }-algebra, and composition is biconvex (i.e convex in each variable separately). If \mathcal {C} \to \mathcal {D} is a functor between externally iterable coinflip Markov categories which preserves the coinflip (eg if \mathcal {C}, \mathcal {D} are distributive), it automatically preserves this structure.