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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 7th 2011
    • (edited Dec 7th 2011)

    I noticed that cell complex was missing, so I created it

    • CommentRowNumber2.
    • CommentAuthorbranpk
    • CommentTimeJun 25th 2025
    • (edited Jun 25th 2025)

    The current definition is “a transfinite composition of pushouts of the generating cofibrations”. Should this be “a transfinite composition of pushouts of coproducts of the generating cofibrations”? I think equivalence of these definitions requires AC.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2025
    • (edited Jun 26th 2025)

    That’s the definition as stated in Hovey 1999 Def. 2.1.9 and Hirschhorn 2002 Def. 10.5.8.

    The use of non-constructive methods is typically tacitly understood here (already the existence of the classical model structure on topological spaces needs the axiom of choice).

    But I have now expanded a little in the entry and added a Remark on this point (here).

    diff, v20, current

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 26th 2025

    Re #3: The current version says:

    (Note that the axiom of choice is needed already for basic statements in this context, like the very existence of the classical model structure on topological spaces, see there this Lemma).

    Is “needed” actually correct? Do we have a proof that the existence of the Serre–Quillen model structure implies the axiom of choice?

    Both functorial factorizations in the Serre–Quillen model structure, for example, can be constructed using explicit formulas. The existence of liftings might require the axiom of choice, but do we have a proof of this?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2025

    No, I just mean that the Lemma I pointed to is used in the existence proof.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2025

    I have changed “is needed” to “is used”, in that paragraph.

    diff, v21, current