Given a torsion theory (Y,X) in an abelian category C, the reflector I from C
to the torsion-free subcategory X induces a reflective factorisation system (E,
M) on C. It was shown by A. Carboni, G.M. Kelly, G. Janelidze and R. Par\'e
that (E, M) induces a monotone-light factorisation system (E',M*) by
simultaneously stabilising E and localising M, whenever the torsion theory is
hereditary and any object in C is a quotient of an object in X. We extend this
result to arbitrary normal categories, and improve it also in the abelian case,
where the heredity assumption on the torsion theory turns out to be redundant.
Several new examples of torsion theories where this result applies are then
considered in the categories of abelian groups, groups, topological groups,
commutative rings, and crossed modules.Comment: 12 page
