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Dec 14, 2023 at 14:24 comment added LSpice @someguyonthestreet, re, they may not have had anchors in 2010 (I don't know), but they do now! Your comment.
Nov 5, 2010 at 22:24 comment added Steven Gubkin This is really pretty awesome.
Sep 7, 2010 at 2:28 comment added Todd Trimble Well, your first comment on my answer gave me the impression that you were annoyed that I hadn't acknowledged your earlier mention (and if you were, then please accept my apologies). I think the point however is that any interval (toset with distinct top and bottom) induces a left exact geometric realization, so the question still remains: why choose this one? Is there some sort of abstract conceptual reason? The same question applies to the cone monad: for any interval there is an associated cone monad, so what's the reason for choosing [0, 1] as the interval?
Sep 6, 2010 at 23:43 comment added some guy on the street oh, why not is probably that I'm just so thoroughly used to homotopy being about the interval; so that when asked "whence this geometric realization functor" what occurs to me isn't "because the interval is terminal in ...", but rather that the cone monad --- using the interval --- gives a natural topological simplex category. And that's the answer I did give.
Sep 3, 2010 at 2:11 comment added Todd Trimble Yes, I see now that you refer to this result and give a link. Why didn't you write it as an answer? IMO it comes close to answering David's plea for a canonical categorical justification. For example, I mentioned to David in email that the terminal coalgebra for this particular endofunctor could be seen as a universal solution to the problem of constructing an interval which is invariant with respect to subdivision (which may help justify why this particular endofunctor).
Sep 2, 2010 at 22:47 comment added some guy on the street Yes, I mentioned that... (dang! comments have no anchors!)
Aug 27, 2010 at 8:55 history answered Todd Trimble CC BY-SA 2.5