  The present article is devoted to introduce, in a braided monoidal setting,
the notion of module over a relative Rota-Baxter operator. It is proved that
there exists an adjunction between the category of modules associated to an
invertible relative Rota-Baxter operator and the category of modules associated
to a Hopf brace, which induces an equivalence by assuming certain additional
hypothesis. Moreover, the notion of projection between relative Rota-Baxter
operators is defined, and it is proved that those which are called ``strong''
give rise to a module according to the previous definition in the cocommutative
setting.
