  We explain how to attach a coalgebra $\mathcal C$ over a field $k$ to a small
$k$-linear category $\mathsf E$ satisfying suitable finiteness conditions. In
this context, we study full-and-faithfulness of the contramodule forgetful
functor, and describe explicitly the categories of locally finite left
$\mathcal C$-comodules and left $\mathcal C$-contramodules as certain full
subcategories of the category of left $\mathsf E$-modules.
