{{Short description|Type of mathematical category}} In category theory, a branch of mathematics, the '''permutation category'''<ref>{{harvnb|Trimble|n.d.|loc=§ 1}}</ref> 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 <math>S_n</math> and #there are no morphisms from ''m'' to ''n'' if <math>m\neq n</math>.
It is equivalent as a category to the category of finite sets and bijections between them.
== References == {{reflist}} *{{cite web |first=Todd H. |last=Trimble |url=http://math.ucr.edu/home/baez/trimble/trimble_lie_operad.pdf |title=Notes on the Lie operad |website=University of Chicago |access-date=2022-09-27 |ref={{harvid|Trimble|n.d.}}}}
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Category:Category theory