Permutation category

Type of mathematical category

In mathematics, the permutation category[1] 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 {\displaystyle S_{n}} and
  3. 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

  1. ^ Trimble n.d., § 1
  • Trimble, Todd H. "Notes on the Lie operad" (PDF). University of Chicago. Retrieved 2022-09-27.


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