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Nov 10, 2019 at 18:53 comment added Questioner I guess I did do something depending on that mistake! :(
Nov 10, 2019 at 18:36 comment added Valery Isaev @Questioner Oh, also the second part in your condition is too weak. As noted by Charles Rezk, you should also require that the image of $X \simeq Y$ is the original $FX \simeq FY$.
Nov 10, 2019 at 17:55 comment added Questioner Thanks; it's good to know I'm not completely wrong here. Also, I have (-1)-truncated map in my work, but somewhere along the line mixed that up with the characterization of (-1)-truncated homotopy types being either empty or (-2)-truncated. Thank you for correcting that too before I did anything depending on that mistake!
Nov 10, 2019 at 17:53 vote accept Questioner
Nov 10, 2019 at 16:47 history answered Valery Isaev CC BY-SA 4.0