The Combinatorics of Polynomial Functors
Representation Theory
2012-12-17 v2 Algebraic Topology
Rings and Algebras
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.
Cite
@article{arxiv.1211.6035,
title = {The Combinatorics of Polynomial Functors},
author = {Qimh Richey Xantcha},
journal= {arXiv preprint arXiv:1211.6035},
year = {2012}
}