constant functor

Given categories $\mathcal{C}$,$\mathcal{D}$; $d\in \mathcal{D}$ The constant functor $\Delta d:\mathcal{C}\Rightarrow \mathcal{D}$ is the unique functor that maps:

• all objects to $d$, and
• all morphisms to ${\mathrm{id}}_d$.

Functoriality is immediate.

Remarks

This functor is used in the definition of cone.