The aim of this talk is to provide a way to construct left and right induced representations with respect to an internal functor. Speaking more precisely, let $\boldsymbol{C}$ and $\boldsymbol{D}$ be internal categories in a category $\mathcal{E}$ and $f$ an internal functor from $\boldsymbol{D}$ to $\boldsymbol{C}$. For a fibered category $\mathcal{F}$ over $\mathcal{E}$, there is a functor $f^\bullet$ from the category of representations of $\boldsymbol{C}$ over $\mathcal{F}$ to that of $\boldsymbol{D}$ over $\mathcal{F}$ by pulling back representations along $f$. We give a method to construct left and right adjoint functors of $f^\bullet$ under some “mild” conditions on fibered category $\mathcal{F}$.