Weakly polynomial functors

TL;DR

This paper introduces a broad concept of polynomial functors within symmetric monoidal categories with initial units, providing a classification for those up to a certain degree in the context of hermitian spaces.

Contribution

It defines and studies a general notion of polynomial functors and classifies them in the setting of hermitian spaces for degrees up to n.

Findings

Classification of polynomial functors of degree ≤ n in hermitian spaces

Introduction of a general framework for polynomial functors in symmetric monoidal categories

Establishment of a hierarchy of polynomial functors by degree

Abstract

We introduce and study a general notion of polynomial functor from a small monoidal symmetric category whose unit is an initial object and give a classification result of polynomial functors of degree smaller of equal to n modulo those of degree smaller of equal to n-1 in the case of a category of hermitian spaces.