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 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 nforum 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 sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory 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).

nLab > Latest Changes: shape modality

Bottom of Page

1 to 3 of 3

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 7th 2022

    started a section Preservation of some homotopy fiber products spelling out how the shape modality does not preserve all homotopy fiber products but does preserve the two special cases of (a) looping of delooped objects and (b) of homotopy fiber products over cohesively discrete objects.

    Next I’ll add a little new statement, resulting from the combination of these two and the “reverse pasting law”.

    diff, v29, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 7th 2022

    added statement and proof (here) that the shape modality preserves homotopy fibers of discrete over delooped objects.

    diff, v29, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 7th 2022
    • (edited Jul 7th 2022)

    I have added (here) discussion of a key technical result from traditional equivariant principal bundle theory, recast as a condition of the shape modality commuting with looping when applied to mapping stacks between deloopings of certain topological groups.

    (This discussion might also and maybe better go elsewhere, such as at nearby homomorphisms from compact Lie groups are conjugate. Maybe I’ll put the section into an !include file in order to conveniently have it in both places. )

    diff, v31, current

1 to 3 of 3

  1.