Is that arrow supposed to be an equation? If I understand you correctly, the left and right sides are morphisms. It doesn't make sense to have an arrow between morphisms in a category.

For example, the hom-functor \\(\mathrm{hom} : \mathcal{C}^{\text{op}} \times \mathcal{C} \to \mathbf{Set}\\) will take a morphism \\( (f,g) \\) in \\(\mathcal{C}^{\text{op}} \times \mathcal{C}\\) and turn it into a function \\( \mathrm{hom}(f,g) \\), and we have

\[ \mathrm{hom}(f,g) \circ \mathrm{hom}(j,k) = \mathrm{hom}(f \circ h, g \circ k) \]

since the hom-functor is a functor, and there's an \\(\mathrm{op}\\) in the first slot.

For example, the hom-functor \\(\mathrm{hom} : \mathcal{C}^{\text{op}} \times \mathcal{C} \to \mathbf{Set}\\) will take a morphism \\( (f,g) \\) in \\(\mathcal{C}^{\text{op}} \times \mathcal{C}\\) and turn it into a function \\( \mathrm{hom}(f,g) \\), and we have

\[ \mathrm{hom}(f,g) \circ \mathrm{hom}(j,k) = \mathrm{hom}(f \circ h, g \circ k) \]

since the hom-functor is a functor, and there's an \\(\mathrm{op}\\) in the first slot.