Usually a binary relation acts between two different sets. Therefore, an algebraic theory for relations should reflect this kind of typing, i.e., the theory should have a suitable notion of source and target of its elements. A convenient framework for that is given by category theory.
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(2007). Categories Of Relations. In: Goguen Categories. Trends in Logic, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6164-6_4
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DOI: https://doi.org/10.1007/978-1-4020-6164-6_4
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