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 comma 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 finite 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 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).
    • CommentRowNumber1.
    • CommentAuthorTapo
    • CommentTimeDec 30th 2020
    I was looking at the unit conditions for Trimble's tetracategory and encountered a problem when fiddling around trying to extend to U51 and U55. I noticed that the whiskered product cell of the pentagonator modification was the only product cell that would add an "interior vertex" and that each unit condition had a single pentagonator in both the positive and negative paths. When extending Trimble's trees to U51 and U55, it seemed to define unit conditions that would lack a pentagonator in the positive and negative paths, resp.
    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 30th 2020

    I can have a look, but it may be a day or so before I find the time.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 30th 2020

    Before I really drill down and try to produce U 51U_{51} and U 55U_{55} myself (my experience is that it takes at least a couple of hours to do these things), maybe I could ask: are you seeing behavior that you don’t see in the other unit conditions? I’m having a slightly hard time picking up the thread from your description.

    • CommentRowNumber4.
    • CommentAuthorTapo
    • CommentTimeDec 30th 2020
    • (edited Dec 30th 2020)

    Precisely, the other unit conditions contain a single copy of Π\Pi in both paths of product cell and constraint compositions, which doesn’t seem to happen for U 51U_{51} or U 55U_{55}. Also, it seemed that all the product cells and constraints take away a vertex, except for Π\Pi which adds a vertex by creating a pentagon at the top of the cell. For U 51U_{51}, the trees produced a positive path (containing K 5K_{5}) that has U 41U_{41} where the Π\Pi “should” be, but the negative path does have a Π\Pi. In regards to diagrams instead of trees, U 51U_{51} seems to have an arrow from I((xy)(yz)) to (xy)(yz) sort of blocking the pentagon from forming. I’m not sure if these missing vertexes could appear from a product cell or constraint that isn’t Π\Pi.

    • CommentRowNumber5.
    • CommentAuthorTapo
    • CommentTimeDec 30th 2020

    U 55U_{55} has a similar problem, except with the negative path missing the Π\Pi.

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 30th 2020

    Well, I think there’s no help for it but to be able to share actual pictures. I haven’t finished writing down U 51U_{51} today, but I hope to get to that. Might you be able to reach me by email?

    Incidentally, if you’ve managed to produce these things correctly (by my lights) based on the sparse hints in those notes, then I’m impressed. :-)

    It happens occasionally that I meet someone who wants to discuss such things in detail, but it’s pretty rare. So, thanks for your interest.

    • CommentRowNumber7.
    • CommentAuthorTapo
    • CommentTimeDec 31st 2020
    Thank you for reaching out as well!

    Hopefully what I've produced isn't too far off, but I'll go ahead and contact you through email.