Question 9.7.5.1.4 (016A): Must a Pseudomonic and Pseudoepic Functor Be an Equivalence of Categories

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Table of Contents
Part 3: Category Theory
Chapter 9: Categories
Section 9.7: More Conditions on Functors
Subsection 9.7.5: Pseudoepic Functors
Question 9.7.5.1.4: Must a Pseudomonic and Pseudoepic Functor Be an Equivalence of Categories (cite)

Question 9.7.5.1.4 ▶ Must a Pseudomonic and Pseudoepic Functor Be an Equivalence of Categories

A pseudomonic and pseudoepic functor is dominant, faithful, essentially injective, and full on isomorphisms. Is it necessarily an equivalence of categories? If not, how bad can this fail, i.e. how far can a pseudomonic and pseudoepic functor be from an equivalence of categories?

This question also appears as [MO 468334].

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