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Timeline for Segal maps for Segal precategories

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May 29, 2015 at 19:43 vote accept Edoardo Lanari
May 29, 2015 at 19:42 comment added Tyler Lawson @EdoardoLanari Yes, absolutely, you need that a decomposition into disconnected components preserves equivalences.
May 29, 2015 at 19:08 comment added Edoardo Lanari I got your first argument, but I think you also have to prove the homotopy invariance of the construction $X_1(a,b)$, which again follows by discreteness of the $0$-th space (so that, in particular, it does not hold in general).
May 29, 2015 at 17:49 history answered Tyler Lawson CC BY-SA 3.0