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arXiv · 1703.08094

Small presentations of model categories and Vop\v{e}nka's principle

G. Raptis·J. Rosický
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Abstract

We prove existence results for small presentations of model categories generalizing a theorem of D. Dugger from combinatorial model categories to more general model categories. Some of these results are shown under the assumption of Vop\v{e}nka's principle. Our main theorem applies in particular to cofibrantly generated model categories where the domains of the generating cofibrations satisfy a slightly stronger smallness condition. As a consequence, assuming Vop\v{e}nka's principle, such a cofibrantly generated model category is Quillen equivalent to a combinatorial model category. Moreover, if there are generating sets which consist of presentable objects, then the same conclusion holds without the assumption of Vop\v{e}nka's principle. We also correct a mistake from previous work that made similar claims.

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G. Raptis, J. Rosický. 2017-03-23. Small presentations of model categories and Vop\v{e}nka's principle. https://arxiv.org/abs/1703.08094

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