In mathematics, the permutation category
is a
category
Category, plural categories, may refer to:
General uses
*Classification, the general act of allocating things to classes/categories Philosophy
* Category of being
* ''Categories'' (Aristotle)
* Category (Kant)
* Categories (Peirce)
* Category ( ...
where
#the objects are the natural numbers,
#the morphisms from a natural number ''n'' to itself are the elements of the
symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric grou ...
and
#there are no morphisms from ''m'' to ''n'' if
.
It is
equivalent as a category to the category of finite sets and bijections between them.
References
*
{{categorytheory-stub
Category theory