A `double category of relations' is defined in this paper as a cartesian equipment in which every object is suitably discrete. The main result is a characterization theorem that a `double category of relations' is equivalent to a double category of relations on a regular category when it has strong and monic tabulators and a double-categorical subobject comprehension scheme. This result is based in part 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 "functionally complete bicategory of relations" or a "tabular allegory".
Keywords: double categories, bicategories, relations, cartesian equipments, Frobenius Law
2020 MSC: 18N10, 18N25
Theory and Applications of Categories, Vol. 38, 2022, No. 33, pp 1249-1283.
Published 2022-11-03.
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