Permutation category

In mathematics, the permutation category 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 $$S_n$$ 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.