[002Q] Definition 4·c (Uniform Yoneda structure).

We call uniform Yoneda structure on $\mathbb K$ a Yoneda structure as defined above in the sense of (Street & Walters, 1978), where in addition

  • each extension $\chi^f$ is pointwise;
  • for every $g : B\to PC$ there exists $Z$ and $B\xto{b} Z \xto{c} C$ such that $g = Pc\circ Y_Z\circ b$.

Examples of such structure: $\Cat$, uniform cosmoi of (Street, 1974).