Polynomial Functors on Pointed Categories

TL;DR

This paper classifies polynomial functors from categories with zero objects and finite sums into abelian categories, extending to categories with sums and a regular projective generator.

Contribution

It provides a comprehensive classification of polynomial functors in pointed categories, including those with sums and a small, regular projective generator.

Findings

Classification of polynomial functors in pointed categories.

Extension of classification to categories with sums and a projective generator.

Framework for understanding functors in abelian categories.

Abstract

A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to include functors from a category with sums and a zero object, carrying a small, regular projective generator.