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Erratum to: “Small presentations of model categories and Vopěnka’s principle”. (English) Zbl 1475.18007

Summary: The proof of Theorem 3.1(3) in our paper [ibid. 20, No. 1, 303–328 (2018; Zbl 1388.18004)] turns out to be invalid due to a recent correction [J. Adámek et al., Commentat. Math. Univ. Carol. 60, No. 4, 447–462 (2019; Zbl 1474.18012)] of a result from [J. Adámek and J. Rosický, Locally presentable and accessible categories. Cambridge: Cambridge University Press (1994; Zbl 0795.18007)] 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 Theorem 3.1(3) [the authors, loc. cit.] and explain that the rest of the results of [the authors, loc. cit.] hold with essentially the same proofs.

MSC:

18C35 Accessible and locally presentable categories
18N40 Homotopical algebra, Quillen model categories, derivators
55U35 Abstract and axiomatic homotopy theory in algebraic topology
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