Given a displayed category over a category $\mathrm{𝒞︀}$ and a functor $𝐹:\mathrm{𝒟︀}\to \mathrm{𝒞︀}$, the reindexing of along $𝐹$ is a displayed category over $\mathrm{𝒟︀}$. It is simply the portion of over the image of $𝐹$.