Yes, Ellerman reinvented profunctors and then I told him "those are profunctors".

[Bénabou](https://fr.wikipedia.org/wiki/Distributeur_(th%C3%A9orie_des_cat%C3%A9gories)) was the first to invent them, in 1973, and he called them both profunctors and 'distributors', or more precisely 'profoncteurs' and 'distributeurs'. The Australians like to call them 'bimodules' or simply 'modules' for short. (A bimodule in ring theory is an example of an enriched profunctor).