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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 29th 2016

    I have split off an entry homotopy in a model category from homotopy and then spelled out statement and proof of the basic lemmas.

  1. There was a mistake.

    Béranger Seguin

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeApr 26th 2021

    In the lemma

    Let XX be cofibrant. If there is a left homotopy f Lgf \Rightarrow_L g then there is also a right homotopy f Rgf \Rightarrow_R g (def. \ref{LeftAndRightHomotopyInAModelCategory}) with respect to any chosen path object.

    I believe the chosen path object must also be good. (Otherwise, YY itself is a non-good path object, and a right homotopy with respect to it would say f=gf=g.)

    diff, v4, current