A note on the relation between categories and hyperstructures

摘要

In this paper, first we introduce the categories of “n-ary hyperstructures” ( HS n {{mathrm{HS}}_{n}} ) and “n-ary hyperstructures with particular carriers and relations” ( HSP n {{mathrm{HSP}}_{n}} ), and we prove that the categories of HS n {{mathrm{HS}}_{n}} and HSP n - 1 {{mathrm{HSP}}_{n-1}} are isomorphic. Then we prove that the category of “ ( n - 1 ) {(n-1)} -ary hypergroupoids” ( HG n - 1 {{mathrm{HG}}_{n-1}} ) is a full subcategory of the category HS n {{mathrm{HS}}_{n}} and the category of “unary binding n-ary algebra with particular properties” ( UBA n {{mathrm{UBA}}_{n}} ) is a full subcategory of the category HSP n {{mathrm{HSP}}_{n}} . Next, we define two functors F and G, and show that the restriction of the functor F to the category HG n {{mathrm{HG}}_{n}} is an isomorphism of HG n {{mathrm{HG}}_{n}} onto