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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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
Have added the observation (here) that $Maps(X,-)$ out of a $G$-CW-complex $X$ is a right Quillen endofunctor on $G$-spaces equipped with the fine model structure:
$G Act\big( TopSp_{Qu}\big)_{fine} \underoverset {\underset{Maps(X,-)}{\longrightarrow}} {\overset{X \times (-)}{\longleftarrow}} {\bot_{\mathrlap{Qu}}} G Act\big( TopSp_{Qu}\big)_{fine}$Can this be cited directly from the literature? I haven’t yet found a reference that makes it explicit.
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…
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.
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