The symmetric monoidal 2-category of permutative categories

TL;DR

This paper introduces a tensor product for permutative categories, establishing that the 2-category of these categories forms a closed symmetric monoidal bicategory, advancing the understanding of their algebraic structure.

Contribution

It defines a tensor product for permutative categories and proves that this makes their 2-category a closed symmetric monoidal bicategory.

Findings

The tensor product for permutative categories is well-defined.

The 2-category of permutative categories is closed symmetric monoidal.

Key properties of the tensor product are established.

Abstract

We define a tensor product for permutative categories and prove a number of key properties. We show that this product makes the 2-category of permutative categories closed symmetric monoidal as a bicategory.