nLab
permutation groupoid

The permutation groupoid, sometimes denoted \mathbb{P}, is a skeleton of the groupoid of finite sets and bijections. Namely:

= n0S n, \mathbb{P} = \bigsqcup_{n \ge 0} S_n \, ,

where objects are natural numbers, all morphisms are automorphisms, and the automorphism group of the object nn is the symmetric group S nS_n.

In other words, \mathbb{P} is equivalent to the core of FinSet.

There are many notations for \mathbb{P} besides ‘\mathbb{P}’, such as SS and Σ\Sigma. In The Joy of Cats, \mathbb{P} is denoted BijBij.

Revised on July 9, 2010 01:22:17 by Toby Bartels (173.60.119.197)