Poloids from the Points of View of Partial Transformations and Category Theory

TL;DR

This paper explores poloids, a mathematical structure encompassing monoids and groupoids, from the perspectives of category theory and partial transformations, highlighting their dual representations and properties.

Contribution

It provides a dual perspective on poloids, connecting category theory and partial transformation representations, which enhances understanding of their structure.

Findings

Poloids can be viewed as one-sorted categories.

Poloids can be represented by partial magmas of partial transformations.

The paper bridges the perspectives of category theory and partial transformations.

Abstract

Monoids and groupoids are examples of poloids. On the one hand, poloids can be regarded as one-sorted categories; on the other hand, poloids can be represented by partial magmas of partial transformations. In this article, poloids are considered from these two points of view.