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 $\mathcal{C}$ and $\mathcal{D}$ be internal categories in a category $\mathcal{E}$ and $f$ an internal functor from $\mathcal{D}$ to $\mathcal{C}$. For a fibered category $\mathcal{F}$ over $\mathcal{E}$, there is a functor $f^*$ from the category of representations of $\mathcal{C}$ over $\mathcal{F}$ to that of D over F by pulling back representations along f. We give a method to construct left and right adjoint functors of $f^*$ under some “mild” conditions on fibered category $\mathcal{F}$.