  We prove that the KLR algebra associated with the cyclic quiver of length $e$
is a subquotient of the KLR algebra associated with the cyclic quiver of length
$e+1$. We also give a geometric interpretation of this fact. This result has an
important application in the theory of categorical representations. We prove
that a category with an action of $\widetilde{\mathfrak{sl}}_{e+1}$ contains a
subcategory with an action of $\widetilde{\mathfrak{sl}}_{e}$. We also give
generalizations of these results to more general quivers and Lie types.
