Summary: On a category \(\mathscr{C}\) with a designated (well-behaved) class \(\mathcal{M}\) of monomorphisms, a closure operator in the sense of D. Dikranjan and E. Giuli is a pointed endofunctor of \(\mathcal{M}\), seen as a full subcategory of the arrow-category \(\mathscr{C}^{\mathbf{2}}\) whose objects are morphisms from the class \(\mathcal{M}\), which “commutes” with the codomain functor \(\mathsf{cod}\colon \mathcal{M}\to \mathscr{C}\). In other words, a closure operator consists of a functor \(C\colon \mathcal{M}\to\mathcal{M}\) and a natural transformation \(c\colon 1_\mathcal{M}\to C\) such that \(\mathsf{cod} \cdot C=C\) and \(\mathsf{cod}\cdot c=1_{\mathsf{cod}}\). In this paper we adapt this notion to the domain functor \(\mathsf{dom}\colon \mathcal{E}\to\mathscr{C}\), where \(\mathcal{E}\) is a class of epimorphisms in \(\mathscr{C}\), and show that such closure operators can be used to classify \(\mathcal{E}\)-epireflective subcategories of \(\mathscr{C}\), provided \(\mathcal{E}\) is closed under composition and contains isomorphisms.