Homology, Homotopy and Applications

Volume 23 (2021)

Number 2

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

Pages: 375 – 378

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n2.a20


G. Raptis (Fakultät für Mathematik, Universität Regensburg, Germany)

J. Rosický (Department of Mathematics and Statistics, Faculty of Sciences, Masaryk University, Brno, Czech Republic)


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.


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

2010 Mathematics Subject Classification

18C35, 55U35

Received 10 October 2020

Accepted 13 July 2021

Published 29 September 2021