Groupoids assigned to relational systems
Ivan Chajda, Helmut Länger · Mathematica Bohemica · 2013
By a relational system we mean a couple $(A,R)$ where $A$ is a set and $R$ is a binary relation on $A$, i.e.\ $R\subseteq A\times A$. To every directed relational system $\mathcal {A}=(A,R)$ we assign a groupoid ${\mathcal G}({\mathcal A})=(A,\cdot )$ on the same base set where $xy=y$ if and only if $(x,y)\in R$. We characterize basic properties of $R$ by means of identities satisfied by ${\mathcal G}({\mathcal A})$ and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems.