Double Categories of Relations

By Michael Lambert. Theory and Applications of Categories, 2021

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A double category of relations is essentially a cartesian equipment with strong, discrete and functorial tabulators and for which certain local products satisfy a Frobenius Law. A double category of relations is equivalent to a double category whose proarrows are relations on some ordinary category admitting a proper and stable factorization system. This characterization is based closely on the recent characterization of double categories of spans due to Aleiferi. The overall development can be viewed as a double-categorical version of that of the notion of a"tabular allegory"or that of a"functionally complete bicategory of relations."

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

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