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 book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus 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 homology 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 monads monoidal monoidal-category-theory morphism motives motivic-cohomology newpage nforum 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 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
    • CommentTimeDec 17th 2009

    Jim Stasheff pointed out a reference that discusses categorifications of associahedra. I added the ref to associahedron

    • CommentRowNumber2.
    • CommentAuthorColin Tan
    • CommentTimeMay 9th 2014

    Urs, this link at associahedron to the reference by Forcey you mentioned is currently broken.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 9th 2014

    Colin, with broken links, Google is your friend. Here it gives us this:

    • Stefan Forcey, Quotients of the multiplihedron as categorified associahedra, Homology Homotopy Appl. Volume 10, Number 2 (2008), 227-256. (Euclid)
    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 17th 2015

    I have added an abstract description of (barycentrically subdivided) associahedra, in terms of a bar construction, to the definition section of associahedron. This is actually a definition, which wasn’t really there before.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeMar 17th 2015


  1. I added a pointer/short description of Loday’s concrete realization of the associahedron as a convex hull of integer coordinates. I wonder how it relates to the construction Todd gave above?

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 25th 2015

    Good question. I believe Stefan Forcey has worked on bridging these sorts of abstract and concrete descriptions of polyhedra that arise in operadic combinatorics. You’re right that some effort to go into this should be entered at the nLab.

  2. The links under “Rotatable illustrations of some Stasheff polyhedra…” seem to be dead. I could be wrong, so I won’t remove them, although I did explore them and could not find rotatable polyhedra. For separate reasons I recently made a 3D rotatable associahedra app for the first 10 associahedra, and given that these links seem to be dead, I thought I would share.


    diff, v30, current

  3. That app is very cool! Thanks for adding! It brings home the impossibility of dealing with higher categories purely combinatorically! I agree that we can tweak the old links, I will do that now.

    • CommentRowNumber10.
    • CommentAuthorRichard Williamson
    • CommentTimeOct 17th 2020
    • (edited Oct 17th 2020)

    Updating and otherwise tweaking links to visualisations of Stasheff polyhedra, giving preference to the fantastic app linked to in the previous edit!

    diff, v31, current

  4. The picture of K 4K_4 doesn’t display too well on a mobile. We should replace it by a Tikz figure; I think I have already created such a figure somewhere else on the nLab, I’ll see if I can find it later (or someone else is welcome to do so if they have time!).

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)