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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 31st 2023

    starting something, but just a couple of references so far

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 17th 2023

    made a note (here) that:

    The model category Sp ΣSp^\Sigma_{\mathcal{R}} of parameterized spectra given in Hebestreit, Sagave & Schlichtkrull (2020) is not quite right proper (cf. pp. 40) but, in its version based on simplicial sets, left base change f *f^\ast along Kan fibrations f:B 1B 2f \,\colon\, B_1 \to B_2 of (zero-spectrum bundles over) Kan complexes is a left Quillen functor between the slice model structures (by HSS20, Lem 7.22).

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 17th 2023

    Under “Properties” (here) I have started a list with some facts extracted from Hebestreit, Sagave & Schlichtkrull (2020).

    I’d like to conclude that the last base change Quillen adjoint triple generalizes to module spectra. This should follow immediately if the monoid axiom holds in the positive local model structure based on simplicial sets. That this is the case seems to be at least implicit in their text, such as from the last line on p. 30 (which laments that the monoid axioms fails with respect to topological spaces) – but I am not sure.

    diff, v6, current