On mono-unary algebras corresponding to n-ary groupoids

TL;DR

This paper generalizes a construction linking n-ary groupoids to mono-unary algebras, introducing a functor between their categories and exploring homomorphisms, expanding the theoretical framework of algebraic structures.

Contribution

It introduces a functor from n-ary groupoids to mono-unary algebras and generalizes homomorphism constructions, extending Novotný's original method.

Findings

Defined a functor from n-ary groupoids to mono-unary algebras

Constructed homomorphisms between n-ary groupoids

Extended Novotný's method to a broader class of algebraic structures

Abstract

In this paper we modify and generalize a construction presented by Novotn\'y: given a groupoid (a set equipped with a binary operation), it is defined a mono-unary algebra corresponding to that specific groupoid. We shall introduce and study a functor from the category of n-ary groupoids to the category of mono-unary algebras. The main result of this paper concerns the construction of homomorphisms between n-ary groupoids, a natural generalization of the method presented by Novotn\'y.