Sometimes people write $R\colon X$⇸$Y$ or $R\colon X$↬$Y$. The former is frequently used for morphisms in a category (like the category Rel of sets and relations) which are "like relations, bimodules, or profunctors" rather than like functions, homomorphisms or functors. The latter is used in the chapter on allegories in Sketches of an Elephant; I don't know if it's more widely used.
Mike Shulman
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