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 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 topological 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: simplicial localization

Bottom of Page

1 to 10 of 10

  1.  
    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeApr 5th 2013

    Someone deleted the contents of the entry simplicial localization on th 4 April, then another reinstated it on the 5th. Curious!

    • CommentRowNumber2.
    • CommentAuthorZhen Lin
    • CommentTimeApr 5th 2013

    I added in the definition of “standard” simplicial localisation.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 5th 2013
    • (edited Apr 5th 2013)

    @ZhenLin: thanks! Great.

    I have added some hyperlinks.

    (I thought we did have an entry “relative category”, but apparently we don’t. But I think somewhere on the nLab these are discussed a little. Can’t search right now, as I have to run.)

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeMay 1st 2021
    I think there should include some dicussions about the unversal property of the simplicial localisations, e.g. Remark 2.2.1 of Bertrand Toën and Gabriele Vezzosi's paper Homotopical Algebraic Geometry I: Topos Theory.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 1st 2021

    You are invited to try your hand on something. Hit “edit” at the bottom of the page to edit the source.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2021

    added pointer to:

    diff, v36, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2021

    added statement (here) on Quillen equivalences inducing DK equivalences

    diff, v38, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 31st 2023
    • (edited May 31st 2023)

    added DOIs to all the Dwyer & Kan-references

    diff, v44, current

  9. Changed the proposition directly under “### Simplicial localization of model categories”: the equivalence of (∞,1)-categories between the (bifibrant subcategory of) a simplicial model category and its simplicial localization at the weak equivalences only works if you let the former be a sSet-category, not a Set-category. This is also what Dwyer-Kan have in their paper, see property (iv) on their first page.

    Arthur Pander Maat

    diff, v46, current

1 to 10 of 10

  1.