Abstract
Under GCH, a set functor F does not preserve finite unions of non-empty sets if and only if the category Coalg F of all F-coalgebras is universal. Independently of GCH, we show that for any non-accessible functor F preserving intersections, the category Coalg F has a large discrete full subcategory, and we give an example of a category of F-coalgebras that is not universal, yet has a large discrete full subcategory.
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The first author gratefully acknowledges the support of the project 1M0022162080 of the Czech Ministry of Education. The second author gratefully acknowledges the support provided by the NSERC of Canada. The third author gratefully acknowledges the support of the project MSM 0021620839 of the Czech Ministry of Education.
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Koubek, V., Sichler, J. & Trnková, V. Universality of Categories of Coalgebras. Appl Categor Struct 19, 939–957 (2011). https://doi.org/10.1007/s10485-010-9232-1
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DOI: https://doi.org/10.1007/s10485-010-9232-1