Example. Making endofunctors for algebraic data types [dt-0051]

\begin {array}{llr} \textsf {Object mapping} & \textsf {Morphism mapping}\\[0.2em] \mathcal {F}(X) = X + \mathbf {1} & \mathcal {F}(f) = f + \mathsf {id}_\mathbf {1} & \quad \quad \text {((co)-natural numbers)} \\ \mathcal {F}(X) = \mathbf {1} + (\mathbb {Z}_\bot \times X) & \mathcal {F}(f) = \mathsf {id}_\mathbf {1} + (\mathsf {id}_{\mathbb {Z}_\bot } \times f) & \text {((co)-lists of integers)}\\ \end {array}