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Nov 27, 2017 at 8:50 comment added Harry Gindi Yeah, I was able to see it was invertible if it was homotopic and that it was a fibre square when they are Kan complexes since the overcategory of a Kan complex is contractible. What was weird is that the formula for that fibre is exactly the category of cones in Y from the vertex p to f when they are ordinary categories and also presumably infty-categories. The commutativity was what was unclear to me, and it seems like one really needs to unwind one definition of the Kan extension and prove it down in the details.
Nov 27, 2017 at 8:42 vote accept Harry Gindi
Nov 27, 2017 at 8:42 vote accept Harry Gindi
Nov 27, 2017 at 8:42
Nov 27, 2017 at 7:47 history answered Rune Haugseng CC BY-SA 3.0