Definable orthogonality classes in accessible categories are small

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Authors

BAGARIA J. CASACUBERTA Carles MATHIAS A. R. D. ROSICKÝ Jiří

Year of publication 2015
Type Article in Periodical
Magazine / Source Journal of the European Mathematical Society
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.4171/JEMS/511
Field General mathematics
Keywords supercompact cardinal; extendible cardinal; Lévy hierarchy; accessible category; reflective subcategory
Description We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopěnka's principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Lévy hierarchy.
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