Permutation category

In mathematics, the permutation category^[1] is a category where

1. an object is a natural number,
2. a morphism ${\displaystyle n\to m}$ is an element of the symmetric group ${\displaystyle \Sigma _{n}}$ when ${\displaystyle n=m}$ and is none otherwise.

It is equivalent as an category to the category of finite sets and bijections between them.

References[]

• Todd Trimble, Notes on operads and the Lie operad

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