Quotients and homomorphisms of relational systems

Ivan Chajda; Helmut Länger

Groupoids assigned to relational systems

Ivan Chajda, Helmut Länger (2013)

Mathematica Bohemica

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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 $𝒜 = (A, R)$ we assign a groupoid $𝒢 (𝒜) = (A, \cdot)$ on the same base set where $x y = y$ if and only if $(x, y) \in R$ . We characterize basic properties of $R$ by means of identities satisfied by $𝒢 (𝒜)$ and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems.

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