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.