# Tensor product of correspondence functors

## TL;DR

This paper explores the tensor product structure of correspondence functors, demonstrating that those associated with finite lattices form commutative algebras within the tensor category.

## Contribution

It introduces the tensor product of correspondence functors and proves that functors from finite lattices are commutative algebras in this context.

## Key findings

- Correspondence functors can be tensor-multiplied with well-defined properties.
- Functor associated with finite lattices forms a commutative algebra.
- Main properties of the tensor product are established.

## Abstract

As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra in the tensor category of all correspondence functors.