Additive polynomial superfunctors and cohomology

TL;DR

This paper classifies additive polynomial superfunctors and derives formulas to compute extensions involving classical polynomial functors composed with additive superfunctors, linking new results to classical extension theory.

Contribution

It provides a classification of additive polynomial superfunctors and establishes a formula relating their extensions to classical polynomial functor extensions.

Findings

Classification of additive polynomial superfunctors

Extension formulas relating to classical polynomial functors

Conjecture on potential generalizations

Abstract

We prove a classification of additive polynomial superfunctors, which allows us to compute some extensions of a superfunctor of the form $F \circ A$ where $F$ is a classical polynomial functor and $A$ is additive. We get a formula which relates these extensions to the classical ones of $F$. A possible generalisation is conjectured at the end.