The Combinatorics of Polynomial Functors

Abstract

We propose a new description of Endofunctors of Module Categories, based upon a combinatorial category comprising finite sets and so-called mazes. Polynomial and numerical functors both find a natural interpretation in this frame-work. Since strict polynomial functors, according to the work of Salomonsson, are encoded by multi-sets, the two strains of functors may be compared and contrasted through juxtaposing the respective combinatorial structures, leading to the Polynomial Functor Theorem, giving an effective criterion for when a numerical (polynomial) functor is strict polynomial.