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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeSep 10th 2011

    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)(E,M), the class MM 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?