For questions related to profunctors. If $C$ and $D$ are categories, then a profunctor from $C$ to $D$ is a functor of the form $H^F:D^{op}×C→\text{Set}$.
The concept of profunctor is a generalization of the concept of functor in much the same way that the concept of bimodule generalizes that of algebra homomorphism (in fact, this may be understood as a special case of enriched profunctors).
If $C$ and $D$ are categories, then a profunctor from $C$ to $D$ is a functor of the form $$H^F:D^{op}×C→\text{Set}$$ Such a profunctor is usually written as $F:C⇸D$. For $d∈D$ and $c∈C$ the set $H^F(d,c)$ is also called the set of heteromorphisms from $d$ to $c$.
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