Permutation category

In mathematics, the permutation category[1] is a category where

1. an object is a natural number,
2. a morphism ${\displaystyle n\to m}$ is an element of the symmetric group ${\displaystyle \Sigma _{n}}$ when ${\displaystyle n=m}$ and is none otherwise.

It is equivalent as an category to the category of finite sets and bijections between them.