Tensor products of finitely presented functors

TL;DR

This paper develops a unified, constructive approach to tensor products of finitely presented functors, utilizing multilinear universal properties and comparing with Day convolution, with potential applications across different mathematical contexts.

Contribution

It introduces a multilinear universal property framework for tensor products of finitely presented functors and compares it with Day convolution, providing a versatile, constructive methodology.

Findings

Established a multilinear universal property for tensor products

Compared tensor product constructions with Day convolution

Provided a unified, constructive approach for implementation

Abstract

We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions with the Day convolution of arbitrary functors. Our results are stated in a constructive way and give a unified approach for the implementation of tensor products in various contexts.