We give a characterisation of the “Smith is Huq” condition for a pointed Mal’tsev category C by means of a property of the fibration of points, namely: any change of base functor reflects commuting of normal subobjects.
Bourn, D., Martins-Ferreira, N., & Van der Linden, T. (2013). A characterisation of the “Smith is Huq” condition in the pointed Mal’tsev setting. Cahiers de Topologie et Geometrie Differentielle Categoriques, 54(3), 163-183. https://hdl.handle.net/2078.5/61259 (Original work published 2013)