Question 7.2.1.1.2 (00NM): Existence of Specific Left Kan Extensions of Relations

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Table of Contents
Part 2: Relations
Chapter 7: Constructions With Relations
Section 7.2: Kan Extensions and Kan Lifts in the $2$-Category of Relations
Subsection 7.2.1: Left Kan Extensions in $\textbf{Rel}$
Question 7.2.1.1.2: Existence of Specific Left Kan Extensions of Relations (cite)

Question 7.2.1.1.2 ▶ Existence of Specific Left Kan Extensions of Relations

Given relations $S\colon A\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}X$ and $R\colon A\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}B$, is there a characterisation of when the left Kan extension

\[ \text{Lan}_{S}\webleft (R\webright )\colon B\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}X \]

exists in terms of properties of $R$ and $S$?

This question also appears as [MO 461592].

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