# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1705.00914