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Double Categories of Relations

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arxiv 2107.07621 v2 pith:XXHWMUAM submitted 2021-07-15 math.CT

Michael Lambert This is my paper · ORCID
classification math.CT
keywords doublerelationscategorycategoriescharacterizationadmittingaleiferiallegory
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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."

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Cited by 1 Pith paper

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  1. Quantification in Double-Categorical Database Schemas

    math.CT 2026-08 conditional novelty 5.0 of 10

    A rich class of double ologs with dependent products and tabulators interprets first-order modal logic and description logic, and categorically expresses relational division and pushdown query optimizations.

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