Abstract
In any finitely complete category, there is an internal notion of normal monomorphism. We give elementary conditions guaranteeing that a normal section s: Y → X of an arrow f: X → Y produces a direct product decomposition of the form X ≃ Y × W. We then show how these conditions gradually vanish in various algebraic contexts, such as Maltsev, protomodular and additive categories.
Notes
aThese two conditions are equivalent to the fact that τ is an isomorphism.
#Communicated by A. Facchini.