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).
Bibliography
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Street, R., & Walters, R. (1978). Yoneda structures on 2-categories. Journal of Algebra, 50(2), 350–379. https://doi.org/10.1016/0021-8693(78)90160-6Details
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Street, R. (1974). Elementary cosmoi I. In Category Seminar (pp. 134–180). Springer Berlin Heidelberg. https://doi.org/10.1007/bfb0063103Details