In category theory, a branch of mathematics, the permutation category[1] is the category where
- the objects are the natural numbers,
- the morphisms from a natural number n to itself are the elements of the symmetric group
S
n
{\displaystyle S_{n}}
and
- there are no morphisms from m to n if
m
≠
n
{\displaystyle m\neq n}
.
It is equivalent as a category to the category of finite sets and bijections between them.
References
- Trimble n.d., § 1
- Trimble, Todd H. "Notes on the Lie operad" (PDF). University of Chicago. Retrieved 2022-09-27.