Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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