Left Kan extensions are dual to right Kan extensions, not under reversal of the direction of functors (the morphisms in $\textup{\textsf{cat}}$), but under reversal of the direction of natural transformations (the 2-morphisms in the 2-category $\textup{\textsf{cat}}$). A left Kan extension may be converted to a right Kan extension by replacing every category by its opposite'': a functor $K \colon \mathsf{C} \to \mathsf{D}$ is equally a functor $K \colon \mathsf{C}^\mathrm{op} \to \mathsf{D}^\mathrm{op}$ but the process of replacing each category by its opposite reverses the direction of natural transformations, because their components are morphisms in the opposites of the target categories.^\mathrm{co} \to \textup{\textsf{cat}}$, whereco’’ is used to denote the dual of a 2-category obtained by reversing the direction of the 2-morphisms but not the 1-morphisms.} A left Kan extension is pointwise, if the corresponding right Kan extension is pointwise: