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Timeline for pullback and fiber sequence

Current License: CC BY-SA 4.0

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Feb 10, 2020 at 11:43 vote accept lab
Jan 21, 2020 at 17:13 answer added John Klein timeline score: 5
Jan 18, 2020 at 14:32 comment added lab @ValeryIsaev Now I see thanks!
Jan 18, 2020 at 14:24 comment added Valery Isaev This is true if one of the loops is inverted before the concatenation in the definition of the map $D \times D \to D$ and the chosen point of $D$ is the trivial loop.
Jan 18, 2020 at 13:49 comment added lab @Max if i understand correctly your comment then the answer is YES ?
Jan 18, 2020 at 13:42 comment added Maxime Ramzi The hofiber of $A\times C\to D$ has a model consisting of points $(a,c)$ together with a homotopy $f(a)g(c)^{-1} \sim *$, so points $(a,c)$ together with a homotopy $f(a)\sim g(c)$, so it amounts to a point in a model of the homotopy pullback $A\times^h_D C$, but $P$ is precisely that homotopy pullback, because $A\to D$ is a fibration.
Jan 18, 2020 at 13:22 history asked lab CC BY-SA 4.0