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looking for a copy of Michel Thiébaud's 1971 thesis Self-Dual Structure-Semantics and Algebraic Categories, which appears to be an early reference for the relationship between the Kleisli construction and profunctors …

In Bénabou's Les distributeurs, in which the bicategory of profunctors is introduced, Bénabou remarks (page 17, quoted below) that $\mathbf{Prof}$ may be viewed as the construction of a bicategory from … (Indeed, for every functor $F : A \to B$ between small categories, we have profunctors $F_* : A \nrightarrow B$ and $F^* : B \nrightarrow A$ given by $F_*(b, a) = B(b, Fa)$ and $F^*(a, b) = B(Fa, b)$, …

Let $P : W° \times Y \to \mathbf{Set}$ and $Q : X° \times V \to \mathbf{Set}$ be profunctors, and let $L : X \to W$ and $R : Y \to V$ be functors. … In particular, it would be useful to prove statements about these "adjunctions with respect to profunctors", for instance giving characterisations of (co)reflective adjunctions with respect to profunctors …

It is well known that a distributor/profunctor $A \not\rightarrow B$, i.e. a functor $B^{\text{op}} \times A \to \mathrm{Set}$, is equivalent to a two-sided discrete fibration from $A$ to $B$. Further …

Let $P$ be a distributor/profunctor from a small category $A$ to a small category $B$, i.e. a functor $P : B^\circ \times A \to \mathrm{Set}$. We may then define a distributor from $[A^\circ, \mathrm{ …