  We show that the tensor product of $\infty$-categories enriched in a suitable
monoidal $\infty$-category preserves colimits in each variable, fixing a
mistake in an earlier paper of Gepner and the author. We also prove that
essentially surjective and fully faithful functors form a factorization system
on enriched $\infty$-categories, and that the tensor product and internal hom
are compatible with this.
