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 beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry goodwillie-calculus 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 history homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory infinity integration-theory internal-categories k-theory kan lie lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology nonassociative 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 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
    • CommentTimeJan 12th 2012

    I am starting higher Segal space (while sitting in a talk by Mikhail Kapranov about them…)

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJan 12th 2012

    There is a similar “recursive” idea in Kontsevich’s definition of (,n)(\infty,n)-categories which he used at the end of 1990s. Unfortunately, it has never been published. I heard one exposition of it, but did not keep much notes.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 17th 2012

    Added the new paper - Higher Segal spaces I.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 18th 2012
    • (edited Dec 18th 2012)

    Eventually we need to add some warning. Apparently the Dycker-Kapranov-style Segal higher spaces are equivalent to (,1)(\infty,1)-operads, certainly not to (,2)(\infty,2)-categories or similar.

    [edit: I have added a warning to the entry.]

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 18th 2012

    This seems to provide a bridge between them and Lurie:

    In analogy to the situation for (,1)(\infty, 1)-categories, there are various models for the notion of an (,2)(\infty, 2)-category. To describe the bicategorical structures appearing in this work, we will use Segal fibrations. In fact, we will also use the dual notion of a coSegal fibration. These and other models for (,2)(\infty, 2)-categories, as well as their relations, are studied in detail in the comprehensive treatment [Lur09b]. (p. 163)

    In 9.3 they associate an (,2)(\infty, 2)-category to a 2-Segal space.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 18th 2012
    • (edited Dec 18th 2012)


    Now I see that the statement that DK 2-Segal spaces are \infty-operads is essentially in the article, in 3.6.

    (We were supposed to discuss the DK-article in our seminar this semester, but somehow we didn’t get around to. Or not yet maybe.)

    • CommentRowNumber7.
    • CommentAuthorTim Campion
    • CommentTimeSep 13th 2018

    The nlab article higher Segal Space is very unclear – there are two completely different, unrelated types of objects that are sometimes referred to as “higher Segal spaces”. One is n-fold Segal Space, a model of (,n)(\infty,n)-categories. The other is the Dyckerhoff-Kapranov notion of a dd-Segal space, which models something like an (,1)(\infty,1)-category, but without uniqueness of composites (for d2d\geq 2), and higher associativity only in dimension dd and above (higher associativity conditions are governed by dd-dimensional polyhedra, related to dd-dimensional field theories).

    The article as it stands refers to both notions. The “Idea” section refers to nn-fold Segal spaces.

    But we already have a separate page for n-fold Segal spaces. So I’m pretty sure the intention was that this page refer to the Dyckrhoof-Kapranov notion, and not the nn-fold Segal space notion. So I think the article needs a major cleanup.

    Does anybody object to making higher Segal spaces discuss only the Dyckerhoff-Kapranov notion (except for adding some discussion of the difference)?

    • CommentRowNumber8.
    • CommentAuthorTim Campion
    • CommentTimeSep 13th 2018

    Removed misleading references to nn-fold Segal spaces and added a bit of material.

    diff, v14, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 13th 2018

    Please feel invited to work on the entry and improve it, as you see the need.

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)