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 definitions 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 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).

Atrium > Mathematics, Physics & Philosophy: What is denoted by operator bold-B in "Differential cohomology in a cohesive ∞-topos"

Bottom of Page

1 to 4 of 4

  1.  
    • CommentRowNumber1.
    • CommentAuthortomr
    • CommentTimeJan 14th 2023
    I am trying to read https://ncatlab.org/schreiber/show/differential+cohomology+in+a+cohesive+topos (in my own path) and I see bold-B in many places (e.g. BH, where H is infinity-topos), but I have not managed to find name or explanation for it. There is place where B (though with indice) is called as de Rham complex, but I can not connect the dots.

    I am seeking just name for bold-B. No explanation is needed here - I will be able then found it myself as much as I need.

  2. I think the bold B stands for the delooping of an object. So for the infinity-topos H, BH would be the delooping of said infinity-topos.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 14th 2023
    • (edited Jan 14th 2023)

    The boldface B is for delooping of infinity-group objects in an infinity-topos H:

    Groups(H)Ω⟵≃⟶BH*/≥1

    according to this Prop.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 14th 2023
    • (edited Jan 14th 2023)

    I write it in boldface to indicate that this delooping is a “geometrically enriched” version of the classical classifying space construction which is traditionally denoted “BG”:

    If H=SmoothGrpd∞ and G a compact Lie group, then the underlying shape of BG (the delooping groupoid Lie groupoid of G) is the classifying space:

    ʃBG≃BG

    This is Prop. 4.1.12 in Equivariant principal infinity-bundles (schreiber). See also around Prop. 0.2.1 there.

1 to 4 of 4

  1.