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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 beenintroduced by N. Gigli to develop a differential calculus on spaces verifyingthe Riemannian Curvature Dimension condition. More precisely, we discuss underwhich conditions an $L^0$-normed $L^0$-module can be viewed as the space ofsections of a suitable measurable Banach bundle and in which sense suchcorrespondence can be actually made into an equivalence of categories.

The Serre-Swan theorem for normed modules