We construct a category of quantum polynomial functors which deforms
Friedlander and Suslin's category of strict polynomial functors. The main aim
of this paper is to develop from first principles the basic structural
properties of this category (duality, projective generators, braiding etc.) in
analogy with classical strict polynomial functors. We then apply the work of
Hashimoto and Hayashi in this context to construct quantum Schur/Weyl functors,
and use this to provide new and easy derivations of quantum (GLm,GLn)
duality, along with other results in quantum invariant theory.Comment: 34 pages, final version to appear in Journal of Algebr
