Permutation Category

In mathematics, the permutation category is a category where
#the objects are the natural numbers,
#the morphisms from a natural number ''n'' to itself are the elements of the symmetric group $S_n$ and
#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

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Category theory