Not signed in (Sign In)

Start a new discussion

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-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 infinity integration integration-theory k-theory lie lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory 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
    • CommentTimeNov 26th 2018
    • (edited Nov 26th 2018)

    It would be nice if the entry were a little more explicit about the slicing theorem

    PSh (𝒞 /p)PSh (𝒞) /yp. PSh_\infty(\mathcal{C}_{/p}) \stackrel{\simeq}{\to} PSh_\infty(\mathcal{C})_{/y p} \,.

    (here)

    In the special case that the small \infty-category 𝒞\mathcal{C} happens to be a small \infty-groupoid and that pp is constant on an object X𝒞X \in \mathcal{C}, it ought to be true that an explicit form of this equivalence is given in semi-HoTT notation by

    ((cγX)(γ))(ccγX(γ) cγX*). \left( (c \overset{\gamma}{\to}X) \;\mapsto\; \mathcal{F}(\gamma) \right) \;\mapsto\; \left( c \;\mapsto\; \array{ \underset{c \underset{\gamma}{\to}X}{\sum} \mathcal{F}(\gamma) \\ \downarrow \\ \underset{c \underset{\gamma}{\to}X}{\sum} \ast } \right) \,.

    This must be an easy theorem in HoTT?

    diff, v18, current

    • CommentRowNumber2.
    • CommentAuthorAlizter
    • CommentTimeNov 26th 2018
    • (edited Nov 26th 2018)

    How would you describe PSh (𝒞)\mathrm{PSh}_\infty(\mathcal{C}) from inside 𝒞\mathcal{C}? I don’t get how this is supposed to be done in HoTT.

    Edit: Nevermind I haven’t read this properly.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)