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-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory gauge-theory gebra geometric 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 string string-theory 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
    • CommentTimeOct 28th 2009

    created stub for simplicial manifold

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 29th 2009

    added the statement that simplicial manifolds are cofibrant in  sPSh(Diff)_{loc} and that every cofibrant object there is weakly equivalent to a simplicial manifold.

    (In view of the tower of classical literature on simplicial manifolds, this is a useful statement to keep in mind...)

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 12th 2009

    corrected the very last sentence at simplicial manifold in the light of my recent discussion with Mike at model structure on simplicial presheaves on cofibrant objecs in the local projective model structure.

    It's still a noteworthy statement, though: every oo-stack on Diff may be presented by a simplicial manifold.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeNov 17th 2009
    The last statement, while well-known in various formalisms, has a nontrivial proof in some of the interpretations of the statement. For example, it assumes a standard strictification result.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 17th 2009
    • (edited Nov 17th 2009)

    What do you have in mind?

    I was thinking of Dugger's cofibrant replacement functor, which works generally. Its existence shows that every simplicial presheaf in the projective model structure is weakly equivalent to one that is degreewise a coproduct of representables.

    There is some discussion behind the scenes, by the way, that statements like this ensure that models like Chris Schommer-Pries' recent finite dim model of the string 2-group have to exist. But of course one should be aware that the general statement by Dugger only ensures that models consisting of possibly uncoutable disjoint unions of manifolds of finite but arbitrary high dimension exist.

    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeDec 24th 2020


    diff, v10, current

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)