Question 6.2.1.1.3 (00NN): Explicit Description of Left Kan Extensions Along Functions

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Table of Contents
Part 2: Relations
Chapter 6: Constructions With Relations
Section 6.2: Kan Extensions and Kan Lifts in the $2$-Category of Relations
Subsection 6.2.1: Left Kan Extensions in $\textbf{Rel}$
Question 6.2.1.1.3: Explicit Description of Left Kan Extensions Along Functions (cite)

Question 6.2.1.1.3 ▶ Explicit Description of Left Kan Extensions Along Functions

As shown in Item 2 of Proposition 6.2.1.1.1, the left Kan extension

\[ \text{Lan}_{R}\colon \mathbf{Rel}\webleft (A,X\webright )\to \mathbf{Rel}\webleft (B,X\webright ) \]

along a relation of the form $R=f^{-1}$ exists. Is there a explicit description of it, similarly to the explicit description of right Kan extensions given in Proposition 6.2.3.1.1?

This question also appears as [MO 461592].

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