Question 8.5.2.1.3 (0127): Better Characterisations of Functors With Full Precomposition

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Table of Contents
Part 3: Category Theory
Chapter 8: Categories
Section 8.5: Conditions on Functors
Subsection 8.5.2: Full Functors
Question 8.5.2.1.3: Better Characterisations of Functors With Full Precomposition (cite)

Question 8.5.2.1.3 ▶ Better Characterisations of Functors With Full Precomposition

Item 5 of Proposition 8.5.2.1.2 gives a characterisation of the functors $F$ for which $F^{*}$ is full, but the characterisations given there are really messy. Are there better ones?

This question also appears as [MO 468121].

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