// Workers AI · dad joke modeWhat did permutation category say? "I'm rearranging my thoughts.

In category theory, a branch of mathematics, the permutation category is the 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 $S_{n}$ and
3. there are no morphisms from m to n if $m\neq n$.

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.