  In the framework of Abstract Differential Geometry, we show that to a given
principal sheaf and a representation of its stuctural sheaf in $A^n$, where A
is a sheaf of associative, commutative, unital algebras (over R or C), we
associate a vector sheaf. Moreover, under some natural assumptions on the
compatibility of the representation with the Maurer-Cartan (or, logarithmic)
differentials of the structural sheaves involved, we also show that the
connections of the principal sheaf induce A-connections of the associated
vector sheaf. We thus recover a result of the classical Differential Geometry
within a purely algebro-topological context, without any smoothness assumption.
