Abstract
We define relations and their composition in a category with (E, M)-factorization structure, with M consisting of monomorphisms, but E not restricted to epimorphisms. We obtain an associativity criterion for composition of relations, and we study functional and induced relations. We show that under our assumptions, the categories of relations on functional and induced relations are isomorphic to the category of relations for the given category.
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Jayewardene, R., Wyler, O. Categories of Relations and Functional Relations. Applied Categorical Structures 8, 279–305 (2000). https://doi.org/10.1023/A:1008651524610
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DOI: https://doi.org/10.1023/A:1008651524610