A \(\mathcal{V}\) functor \(\mathcal{X}\xrightarrow{F}\mathcal{Y}\) between two \(\mathcal{V}\) categories
A function \(Ob(\mathcal{X})\xrightarrow{F}Ob(\mathcal{Y})\) subject to the constraint:
\(\forall x_1,x_2 \in Ob(\mathcal{X}): \mathcal{X}(x_1,x_2) \leq \mathcal{Y}(F(x_1),F(x_2))\)