  We define a functor which gives the "global rank of a quiver representation"
and prove that it has nice properties which make it a generalization of the
rank of a linear map. We demonstrate how to construct other "rank functors" for
a quiver Q, which induce ring homomorphisms (called "rank functions") from the
representation ring of Q to Z. These rank functions give discrete numerical
invariants of quiver representations, useful for computing tensor product
multiplicities of representations and determining some structure of the
representation ring. We also show that in characteristic 0, rank functors
commute with the Schur operations on quiver representations, and the
homomorphisms induced by rank functors are lambda-ring homomorphisms.
