Talk:Blakers–Massey theorem
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what version of the theorem is stated here?
[edit]It seems odd to me that nearly every version of this theorem is stated in terms of excisive triads except this one. While it's true that one can express (X,A,B) in terms of a pushout, there are also pushouts that are not excisive triads. Perhaps after cofibrant replacement there is a dictionary between the two statements, but I find this to be a confusing reference. This issue is confounded in the article when (C,A) is written, when in fact this might not even be a pair of spaces. Perhaps it is better to write f,g as inclusions of CW complexes? — Preceding unsigned comment added by Amejia83 (talk • contribs) 22:07, 5 August 2020 (UTC)
Let me raise this issue again. The version here seems very false to me without further assumptions on our spaces. One can express it this way if either f or g is a cofibration (i.e. the square is a homotopy pushout) but certainly not just this way. Amejia83 (talk) 21:36, 22 June 2021 (UTC)