Functor Dialgebra

Let $F,G:\mathcal{C}\to\mathcal{D}$ be a pair of Functors. An $(F,G)$-dialgebra is a pair of an object $X:\mathcal{C}$ and a map $\alpha:F(X)\to G(X)$.

Functor Dialgebras generalize both Functor Algebras and Functor Coalgebras.