# Questions tagged [profunctors]

The tag has no usage guidance.

24 questions
Filter by
Sorted by
Tagged with
157 views

### Is there a name for this variant of the category of elements of a profunctor?

Let $\mathsf{C}$ be a category and let $P : \mathsf{C}^{\text{op}} \times \mathsf{C} \to \mathsf{Set}$ be a functor. Let $\mathsf{E}$ be the category whose: objects are pairs $(X,x)$, where $X$ is an ...
101 views

### Strictness of two operations on proarrow equipments

There are several equivalent definitions of a profunctor between categories $C$ and $D$. I'm interested in the following two: A functor $C\times D^o \to \text{Set}$ A co-continuous functor between ...
• 563
202 views

• 305
1k views

### A multicategory is a ... with one object?

We all know that A monoidal category is a bicategory with one object. How do we fill in the blank in the following sentence? A multicategory is a ... with one object. The answer is fairly ...
• 877
1 vote
152 views

### Is the category of profunctors $Prof(A,B)$ equivalent to $Prof(B,A)^{op}$?

$\def\Prof{\mathsf{Prof}}\def\Set{\mathsf{Set}}\def\tobar{\mathrel{\mkern3mu \vcenter{\hbox{$\scriptscriptstyle+$}}\mkern-12mu{\to}}}$Let $A$ and $B$ be categories. Define a profunctor $A\tobar B$ to ...
• 464
156 views

### Exponentials of profunctors

Suppose $f:B\to A$ is an exponentiable functor, so that pullback $f^\ast$ has a right adjoint $\Pi_f$. Then $f\times \mathbf{2} : B\times \mathbf{2} \to A\times \mathbf{2}$ is also exponentiable, and ...
• 62.4k
258 views

• 3,083