The right-unique, left-total binary relations are the functions, while the left-unique, right-total ones are their inverses. So, they are the morphisms of $\mathsf{Set}^\mathrm{op}$. Do they have a name too?
2026-03-26 04:34:24.1774499664
Is there a name for the inverses of the functions (i.e for the left-unique, right-total binary relations)?
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I know of no name for these more fundamental than the two you already gave, unless you view $\mathbf{Set}^\mathrm{op}$ as the category of powersets and call them homomorphisms!