# About a General Definition of Profunctor

Given categories $\mathcal{A},\ \mathcal{B}$ let $\mathcal{A}^{<}:=Fun(\mathcal{A}, Set)$ the category of copresheaves on $\mathcal{A}$, let $\mathcal{A}^{>}:=(\mathcal{A}^{op})^{<}$ the category of presheaves on $\mathcal{A}$.

Let $coCont.Fun(\mathcal{A}, \mathcal{B})$ the category of colimit preserving functors (and natural transformations).

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