Erratum to “Small presentations of model categories and Vopěnka’s principle”

The proof of [6, Theorem 3.1(3)] turns out to be invalid due to a recent correction [3] of a result from [1] which was used in our proof. We revise the definition of a strictly cofibrantly generated weak factorization system $(\mathcal{L},\mathcal{R})$ in a cocomplete category $\mathcal{M}$ by requiring that the codomains of the generator $\mathcal{X} \subseteq \mathcal{L}$ are also strictly small relative to $\mathcal{X}$. Using this slightly stronger definition, we give a new proof of [6, Theorem 3.1(3)] and explain that the rest of the results of [6] hold with essentially the same proofs.

Keywords

cofibrantly generated model category, colimit–dense subcategory, Vopěnka’s principle

2010 Mathematics Subject Classification

18C35, 55U35

Full Text (PDF format)

Received 10 October 2020

Accepted 13 July 2021

Published 29 September 2021