Profunctor
In category theory, a branch of mathematics, profunctors are a generalization of relations and also of bimodules. == Definition == A profunctor (also named distributor by the French school and module by the Sydney school) ϕ {\displaystyle \,\phi } from a category C {\displaystyle C} to a category D {\displaystyle D} , written ϕ : C ↛ D {\displaystyle \phi :C\nrightarrow D} , is defined to be a functor ϕ : D o p × C → S e t {\displaystyle \phi :D^{\mathrm {op} }\times C\to \mathbf {Set} } where D o p {\displaystyle D^{\mathrm {op} }} denotes the opposite category of D {\displaystyle D} and S e t {\displaystyle \mathbf {Set} } denotes the category of sets.