Question 7.2.2.1.3 (00NU): Explicit Description of Left Kan Lifts Along Functions

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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 7.2.2: Left Kan Lifts in $\textbf{Rel}$
Question 7.2.2.1.3: Explicit Description of Left Kan Lifts Along Functions (cite)

Question 7.2.2.1.3 ▶ Explicit Description of Left Kan Lifts Along Functions

As shown in Item 2 of Proposition 7.2.2.1.1, the left Kan lift

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

along a relation of the form $R=\text{Gr}\webleft (f\webright )$ exists. Is there a explicit description of it, similarly to the explicit description of right Kan lifts given in Proposition 7.2.4.1.1?

This question also appears as [MO 461592].

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