Discrete dualities for groupoids
We present discrete dualities for groupoid-based algebras and their associated frames starting from a plain groupoid and then expanding step by step its signature and/or axioms assuming existence of a compatible partial ordering, commutativity, associativity, idempotency, existence of the identity element, and existence of left and right residuals of the groupoid operator. In the final section we present a brief overview of lattice-ordered groupoids and provide hints how to obtain discrete dualities for these from the dualities established in the preceding sections and relevant results in the literature.
EUT Edizioni Università di Trieste
Ivo Düntsch, Ewa Orłowska, "Discrete dualities for groupoids" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.53 (2021)", EUT Edizioni Università di Trieste, Trieste, 2021. pp.