Contents Online

# 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

#### Authors

#### Abstract

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

Received 10 October 2020

Accepted 13 July 2021

Published 29 September 2021