The permutation groupoid, sometimes denoted , is a skeleton of the groupoid of finite sets and bijections. Namely:
where objects are natural numbers, all morphisms are automorphisms, and the automorphism group of the object is the symmetric group .
In other words, is equivalent to the core of FinSet.
can be made into a strict symmetric monoidal category with addition as its tensor product, and it is then the free strict symmetric monoidal category on one object (namely ).
There are many notations for besides ‘’, such as and . In The Joy of Cats, is denoted .
Last revised on September 6, 2017 at 07:57:50. See the history of this page for a list of all contributions to it.