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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeSep 10th 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexCreated [[factorization structure for sinks]], and added remarks to [[Grothendieck fibration]], [[M-complete category]], and [[topological concrete category]] about constructing them. Largely I wanted to record the proof of the theorem that in an factorization structure for sinks $(E,M)$, the class $M$ necessarily consists of monomorphisms. It's a nice generalization of Freyd's theorem about complete small categories, which has more of the feel of a useful theorem than of a no-go theorem like Freyd's. At first I thought that the lifting of factorization structures described at [[topological concrete category]] would work for [[solid functors]] too, but then I couldn't see how to do it. Does anyone?

   Created factorization structure for sinks, and added remarks to Grothendieck fibration, M-complete category, and topological concrete category about constructing them. Largely I wanted to record the proof of the theorem that in an factorization structure for sinks $(E,M)$, the class $M$ necessarily consists of monomorphisms. It’s a nice generalization of Freyd’s theorem about complete small categories, which has more of the feel of a useful theorem than of a no-go theorem like Freyd’s.

   At first I thought that the lifting of factorization structures described at topological concrete category would work for solid functors too, but then I couldn’t see how to do it. Does anyone?