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.
Related projects:	Mathematical structures and their physical applications