Summary: Let \(\mathsf{PreOrd}(\mathbb{C})\) be the category of internal preorders in an exact category \(\mathbb{C}\). We show that the pair (\(\mathsf{Eq}(\mathbb{C}),\,\mathsf{ParOrd}(\mathbb{C})\)) is a pretorsion theory in \(\mathsf{PreOrd}(\mathbb{C})\), where \(\mathsf{Eq}(\mathbb{C})\) and \(\mathsf{ParOrd}(\mathbb{C})\) are the full subcategories of internal equivalence relations and of internal partial orders in \(\mathbb{C}\), respectively. We observe that \(\mathsf{ParOrd}(\mathbb{C})\) is a reflective subcategory of \(\mathsf{PreOrd}(\mathbb{C})\) such that each component of the unit of the adjunction is a pullback-stable regular epimorphism. The reflector \(F\): \(\mathsf{PreOrd}(\mathbb{C}) \to \mathsf{ParOrd}(\mathbb{C})\) turns out to have stable units in the sense of Cassidy, Hébert and Kelly, thus inducing an admissible categorical Galois structure. In particular, when \(\mathbb{C}\) is the category \(\mathsf{Set}\) of sets, we show that this reflection induces a monotone-light factorization system (in the sense of [A. Carboni et al., Appl. Categ. Struct. 5, No. 1, 1–58 (1997; Zbl 0866.18003)]) in \(\mathsf{PreOrd(Set)}\). A topological interpretation of our results in the category of Alexandroff-discrete spaces is also given, via the well-known isomorphism between this latter category and \(\mathsf{PreOrd(Set)}\).