Permutation category
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In category theory, a branch of mathematics, the permutation category 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.
- Trimble, Todd H. (PDF). University of Chicago.