Abstract
We prove that every symmetric residuated groupoid is embeddable in a boolean double residuated groupoid. Analogous results are obtained for other classes of algebras, e.g. (commutative) symmetric residuated semigroups, symmetric residuated unital groupoids, cyclic bilinear algebras. We also show that powerset algebras constructed in the paper preserve some Grishin axioms.
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Kołowska-Gawiejnowicz, M. (2014). On Canonical Embeddings of Residuated Groupoids. In: Casadio, C., Coecke, B., Moortgat, M., Scott, P. (eds) Categories and Types in Logic, Language, and Physics. Lecture Notes in Computer Science, vol 8222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54789-8_14
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DOI: https://doi.org/10.1007/978-3-642-54789-8_14
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