Polynomial Functors of Modules

Abstract

We introduce the notion of numerical functors to generalise Eilenberg & MacLane's polynomial functors to modules over a binomial base ring. After shewing how these functors are encoded by modules over a certain ring, we record a precise criterion for a numerical (or polynomial) functor to admit a strict polynomial structure in the sense of Friedlander & Suslin. We also provide several characterisations of analytic functors.