  In this short note we show that representation and character varieties of
discrete groups can be viewed as tensor products of suitable functors over the
PROP of cocommutative Hopf algebras. Such view point has several interesting
applications. First, it gives a straightforward way of deriving the functor
sending a discrete group to the functions on its representation variety, which
leads to representation homology. Second, using a suitable deformation of the
functors involved in this construction, one can obtain deformations of the
representation and character varieties for the fundamental groups of
3-manifolds, and could lead to better understanding of quantum representations
of mapping class groups.
