Universal measuring coalgebra
= Universal measuring coalgebra
{title2=$P(A,B)$}
A terminal <measuring coalgebra>: every measuring map from $C$ factors uniquely through its universal measuring map by a <coalgebra> homomorphism $C\to P(A,B)$. Composition of universal measurings makes $P(A,A)$ a <bialgebra>, with the identity map providing its unit.