The Clowder Project

\[ D \colon \mathcal{I} \to \mathsf{Fun}\webleft (\mathcal{C},\mathcal{D}\webright ) \]

\begin{align*} \operatorname*{\text{lim}}\webleft (D\webright )_{A} & \cong \operatorname*{\text{lim}}_{i\in \mathcal{I}}\webleft (D_{i}\webleft (A\webright )\webright ),\\ \operatorname*{\text{colim}}\webleft (D\webright )_{A} & \cong \operatorname*{\text{colim}}_{i\in \mathcal{I}}\webleft (D_{i}\webleft (A\webright )\webright ), \end{align*}