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 object 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).

nLab > Latest Changes: homotopy limit

Bottom of Page

1 to 7 of 7

  1.  
    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 22nd 2019

    Formatting fix

    diff, v93, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeAug 27th 2022
    • (edited Aug 27th 2022)

    Added:

    Terminology

    In older literature, such as the original work of Bousfield–Kan \cite{BousfieldKan}, the homotopy limit of a diagram X:I→sSetX\colon I\to sSet is defined as the weighted limit

    hom(I/−,X),hom(I/-, X),

    where the weight I/−I/- sends i↦N(I/i)i\mapsto N(I/i), the nerve of the comma category of ii.

    Such a functor must be derived in order to get the correct (homotopy invariant) notion, which in this case amounts to replacing XX with an objectwise weakly equivalent diagram valued in Kan complexes.

    At some point (when?) a shift in terminology happened, and in the modern parlance homotopy limits are commonly assumed to be derived.

    diff, v100, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 27th 2022

    I have added to this addition (here) a link to Bousfield-Kan map and also to the entry’s own section “Resolved (co)ends”.

    diff, v101, current

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeMar 13th 2023

    Corrected obsolete links to updated ones in

    I, localizers, (pdf);

    II, model categories, (pdf);

    III, derivators, (pdf):

    IV, summary on derivators (pdf)

    diff, v103, current

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeOct 5th 2023

    Added:

    diff, v108, current

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeNov 16th 2023

    Added a reference to A general formulation of homotopy limits.

    diff, v109, current

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeDec 16th 2024

    Fixed broken link

    diff, v112, current

1 to 7 of 7

  1.