  We investigate the representations of the hyperalgebras associated to the map
algebras $\mathfrak g\otimes \mathcal A$, where $\mathfrak g$ is any
finite-dimensional complex simple Lie algebra and $\mathcal A$ is any
associative commutative unitary algebra with a multiplicatively closed basis.
We consider the natural definition of the local and global Weyl modules, and
the Weyl functor for these algebras. Under certain conditions, we prove that
these modules satisfy certain universal properties, and we also give conditions
for the local or global Weyl modules to be finite-dimensional or finitely
generated, respectively.
