Fix an endofunctor $𝐹:\mathrm{𝒞︀}\to \mathrm{𝒞︀}$, a coalgebra $𝛾:𝑋\to 𝐹𝑋$ and an algebra $𝛼:𝐹𝐵\to 𝐵$. A hylomorphism (or coalgebra-to-algebra morphism) from $𝛾$ to $𝛼$ is a morphism $ℎ:𝑋\to 𝐵$ satisfying