Andras Borbely: A brief investigation on how we can relate polygroups to traditional algebraic structures

Abstract: 

In the following we are going to look at a generalised notion of groups. These structures, called polystrucures seems to fall a bit short when it
comes to t properly into the classical theme of mathematics. The cause why groups became so deeply researched was that mathematicians found close resemblance between proofs say in matrix theory and permutation theory so it was helpful to nd an abstract way to do these proofs. And group theory showed to be the link. The problem with polystructures is that they lack this "linking" property. But with the right mindset one doesn't have to discard them straight away. We are going to see that most of the important properties of groups can be exhibited in a way or another. Furthermore we will also see that the modern view of mathematics have a place booked for polystructures from the beginning, namely they form a category.