  We propose a category of bundles in order to perform Lagrangian reduction by
stages in covariant Field Theory. This category plays an analogous role to
Lagrange-Poincar\'e bundles in Lagrangian reduction by stages in Mechanics and
includes both jet bundles and reduced covariant configuration spaces.
Furthermore, we analyze the resulting reconstruction condition and formulate
the Noether theorem in this context. Finally, a model of a molecular strand
with rotors is seen as an application of this theoretical frame.
