Tensor structure for Nori motives

TL;DR

This paper develops a tensor product structure for Nori motives using a universal property approach, providing a new construction that enhances the understanding of their tensorial behavior.

Contribution

It introduces a novel tensor product construction for Nori motives via a universal property, extending the framework of additive tensor categories.

Findings

Established a tensor product with a universal property for Nori motives.

Provided an alternative construction for the tensor product on Nori motives.

Enhanced the theoretical understanding of tensor structures in motivic categories.

Abstract

We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.