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Feb 27, 2017 at 5:39 comment added Tim Campion @JiříRosický Thanks, that definitely answers my question! Is it still true under Vopenka that every weak orthogonality class in a locally presentable category yields a weak factorization system? This almost follows from the fact that every injectivity class is weakly reflective under Vopenka.
Feb 26, 2017 at 12:09 comment added Jiří Rosický There are many weak orthogonality classes in locally presentable categories which are not small. For instance, embeddings in posets (see my joint paper with Adámek, Herrlich and Tholen in Appl. Cat. Str. 10 (2002), 237-249).
Feb 23, 2017 at 1:25 history edited Tim Campion
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Feb 22, 2017 at 22:22 history asked Tim Campion CC BY-SA 3.0