(Co)homological vanishing for non-additive representations of a semi-additive category

TL;DR

This paper proves vanishing results for higher extension and torsion groups between linearized additive functors in semi-additive categories, with applications to correspondence functors.

Contribution

It establishes new vanishing theorems for extension groups in semi-additive categories, extending known results to non-additive contexts.

Findings

Higher extension groups vanish under certain conditions.

Torsion groups also vanish in the studied setting.

Applications to the category of correspondence functors.

Abstract

We show the vanishing of higher extension groups and torsion groups between linearisation of additive functors from a semi-additive category satisfying some conditions to a category of vector spaces. In particular, we apply our results to the category of correspondences functors of Bouc-Th\'evenaz.