All Questions

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 $B$. ...

$\newcommand{\sq}{\mathbin{\square}}$The usual composition $S\diamond R$ of two relations $R\colon A⇸B$ and $S\colon B⇸C$ is defined as follows: For each $(a,c)\in A\times C$, we declare $a\sim_{S\...

Cartesian bicategories axiomatize the intuitively evident but mathematically elusive "cartesian" product on bicategories such as Rel, Span, and Prof. An important concept for cartesian ...

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. Suppose that $$P(Lx, y) \cong Q(x, Ry)$$ natural in $...