# Questions tagged [profunctors]

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### Michel Thiébaud's thesis ("Self-Dual Structure-Semantics and Algebraic Categories")

I am 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 ...
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### Prof and the completion of Cat under right adjoints

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 ...
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### Promonoidal categories as $S$-algebras

A promonoidal category is a pseudomonoid in the monoidal bicategory $\bf Prof$, where the monoidal structure is given (on objects) by the product of categories. I would like to show that promonoidal ...
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### References to using profunctors in program analysis?

Profunctors from a category to itself seem like they'd be useful in representing the result of a program analysis; I can imagine a profunctor that given some information about a function it tells you ...
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### In what sense do the categorical trace and coend count fixed points?

According to the nlab, the categorical trace of a 1-endomorphism $F:C\to C$ in a 2-category is the set hom$(1_C, F)$ of global elements of $F$. If $F$ is a functor in the 2-category Cat, the ...
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### Co-ends as a trace operation on profunctors

The n-lab site on profunctors (http://ncatlab.org/nlab/show/profunctor) describes profunctor composition as using a co-end to "trace out" the connecting variable: \$F\circ G := \int^{d\in D} F(-, d) \...