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

1. the objects are the natural numbers,
2. the morphisms from a natural number n to itself are the elements of the symmetric group ${\displaystyle S_{n}}$ and
3. there are no morphisms from m to n if ${\displaystyle m\neq n}$.

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

References

• Trimble, Todd H. "Notes on the Lie operad" (PDF). University of Chicago. Retrieved 2022-09-27.