HoTT/HoTT — pull request #589 by mikeshulman (2014-10-22 17:53:33+00:00)
Title: The modal factorization system

This is a formalization of most of section 7.5 and 7.6 in the book, in the generality of an arbitrary modality. Pleasingly, all the theorems in `hit.Connectedness` that generalize to a modality (mainly, those that don't involve the interaction of multiple values of `n`) could be proven in that generality with essentially cut-and-pasted proofs, while the remaining theorems in `hit.Connectedness` still work where they are with essentially the same proofs (at least once I got the coercions and hints configured correctly). The proof of lemma 7.6.5 is a bit trickier than in the book, because our `O_ind` has only a propositional computation rule. I only found [one mistake](https://github.com/HoTT/book/pull/731) in the book.