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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2021

    am finally giving this its own entry (this used to be treated within the entry on Elmendorf’s theorem)

    but just a stub for the moment

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 13th 2021

    Have added the observation (here) that Maps(X,)Maps(X,-) out of a GG-CW-complex XX is a right Quillen endofunctor on GG-spaces equipped with the fine model structure:

    GAct(TopSp Qu) fine QuMaps(X,)X×()GAct(TopSp Qu) fine G Act\big( TopSp_{Qu}\big)_{fine} \underoverset {\underset{Maps(X,-)}{\longrightarrow}} {\overset{X \times (-)}{\longleftarrow}} {\bot_{\mathrlap{Qu}}} G Act\big( TopSp_{Qu}\big)_{fine}

    Can this be cited directly from the literature? I haven’t yet found a reference that makes it explicit.

    diff, v6, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 14th 2021

    A kind soul on the AlgTop Discord chat (here) kindly points me to proof that the fine model structure in fact does satisfy the pushout product axiom. Have made a brief note and generalized the statement about the internal Hom Quillen adjunction accordingly.

    Will expand further, but first need to chase through an airport now…

    diff, v9, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeSep 14th 2021

    I have now fleshed out remarks on the cartesian monoidal model structure a little more (here).

    Also added more references establishing properness and cofibrant generation and/or topological enrichment.