  We investigate a generalization of the classical notion of a Schur functor
associated to a ribbon diagram. These functors are defined with respect to an
arbitrary algebra, and in the case that the underlying algebra is the
symmetric/exterior algebra, we recover the classical definition of Schur/Weyl
functors, respectively. In general, we construct a family of 3-term complexes
categorifying the classical concatenation/near-concatenation identity for
symmetric functions, and one of our main results is that the exactness of these
3-term complexes is equivalent to the Koszul property of the underlying algebra
$A$. We further generalize these ribbon Schur functors to the notion of a
multi-Schur functor and construct a canonical filtration of these objects whose
associated graded pieces are described explicitly; one consequence of this
filtration is a complete equivariant description of the syzygies of arbitrary
Segre products of Koszul modules over the Segre product of Koszul algebras.
Further applications to the equivariant structure of derived invariants,
symmetric function identities, and Koszulness of certain classes of modules are
explored at the end, along with a characteristic-free computation of the
regularity of a Schur functor applied to the tautological subbundle on
projective space.
