Let $\mathbb K$ be a 2-category equipped with a Yoneda structure in the sense of Street-Walters (Street & Walters, 1978) (see also (Street, 1974)), which means $\mathbb K$ is equipped with a right ideal $\mathbb A\subseteq\mathbb K_1$ of “admissible” 1-arrows, and for every $A\in \mathbb A$ a “Yoneda morphism” $Y_A : A \to PA$ is given so that for each $f : A \to B$ in $\mathbb A$ there is a diagram with the property that

• $\chi^f$ exhibits $B(f,1)$ as the left extension of $Y_A$ along $f$;
• $\chi^f$ exhibits $f$ as the absolute lift of $Y_A$ along $B(f,1)$;
• for every $k : B\to PA$ and $\sigma : B(f,1)\To k$, $\sigma$ is an isomorphism in $\mathbb K$ if and only if $(\sigma * f)\circ \chi^f$ exhibits $f$ as absolute lift of $Y_A$ along $k$.