Permutation category

In mathematics, the permutation category is a category where

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

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

References

• Todd Trimble, Notes on operads and the Lie operad