  We develop a categorical approach to quivers and their modules. Naturally
this leads to a notion of an action of a monoidal category on quivers. Using
this, we construct for a large class of quivers rigid monoidal structures on
their categories of modules. This fusion product on the quiver modules induces
a graded ring structure with duality and trace on the moduli spaces of
semisimple quiver modules. Our approach allows to consider a class of relations
on such fusion quivers that are compatible with the rigid monoidal structure.
In particular we obtain a class of preprojective algebras with fusion product
on their modules.
