  The aim of this note is to analyse the structure of the $L^0$-normed
$L^0$-modules over a metric measure space. These are a tool that has been
introduced by N. Gigli to develop a differential calculus on spaces verifying
the Riemannian Curvature Dimension condition. More precisely, we discuss under
which conditions an $L^0$-normed $L^0$-module can be viewed as the space of
sections of a suitable measurable Banach bundle and in which sense such
correspondence can be actually made into an equivalence of categories.
