Let F : 𝒞 → 𝒞 : 𝐹 → 𝒞 𝒞 F:\mathcal{C}\to\mathcal{C} be an Endofunctor. An F 𝐹 F -algebra is an object A : 𝒞 : 𝐴 𝒞 A:\mathcal{C} and a map α : F ( A ) → A : 𝛼 → 𝐹 𝐴 𝐴 \alpha:F(A)\to A .