Functor Coalgebra

A coalgebra of an Endofunctor $F:\mathcal{C}\to\mathcal{C}$ is a pair of an object $A:\mathcal{C}$ and a map $A\to F(A)$. This is a special case of a Functor Dialgebra; in particular, a $(\mathrm{Id},F)$-dialgebra.