If you have an adjunction between two categories $\mathcal{C}$ and $\mathcal{D}$, and two full subcategories $\mathcal{\Gamma}$ and $\mathcal{\Delta}$ of $\mathcal{C}$ and $\mathcal{D}$ respectively, does that adjunction always restrict to an adjunction between $\mathcal{\Gamma}$ and $\mathcal{\Delta}$?