Geodesic
Double Categories of Relations
Theory and applications of categories, Tome 38 (2022), pp. 1249-1283.

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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".
Publié le :
Classification : 18N10, 18N25
Keywords: double categories, bicategories, relations, cartesian equipments, Frobenius Law 
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     author = {Michael Lambert},
     title = {Double {Categories} of {Relations}},
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Michael Lambert. Double Categories of Relations. Theory and applications of categories, Tome 38 (2022), pp. 1249-1283. http://geodesic.mathdoc.fr/item/TAC_2022_38_a32/