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A note on the relation between categories and hyperstructures

  • Seid Mohammad Anvariyeh EMAIL logo and Samaneh Soltani
Published/Copyright: July 6, 2017

Abstract

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

Keywords: Hyperstructure
MSC 2010: 18C99; 18B40; 18B99

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Received: 2017-3-11
Revised: 2017-5-29
Accepted: 2017-6-7
Published Online: 2017-7-6
Published in Print: 2018-1-1

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