For categories $\mathrm{𝒞︀}$ and $\mathrm{𝒟︀}$, we can define the weakening of $\mathrm{𝒟︀}$ over $\mathrm{𝒞︀}$ as a displayed category over $\mathrm{𝒞︀}$ which trivially displays a copy of $\mathrm{𝒟︀}$ over each object of $\mathrm{𝒞︀}$.