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.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 2nd 2022

    Removed the following discussion:

    Discussion on a previous version of this entry:

    Mike: This term is kind of unfortunate; simplicial weak ω\omega-category could also mean a simplicial object in weak ω\omega-categories. I don’t suppose we can do anything about that?

    Urs: my impression is that what Dominic Verity mainly wants to express with the term is “simplicial model for weak ω\omega-category”. Maybe we could/should use a longer phrase like that?

    Mike: That would make me happier.

    Urs: okay, I changed it. Let me know if this is good now.

    Toby: But what about ’globular ω\omega-category’ and things like that? Doesn't ’simplicial ω\omega-category’ fit right into that framework? This page title sounds like an entire framework for defining ω\omega-category rather than a single ω\omega-category simplicially defined.

    Urs: i am open to suggestions – but notice that it does indeed seem to me that Dominic Verity wants to express “an entire framework for defining ω\omega-category”, namely the framework where one skips over the attempt to define ω\omega-categories and instead tries to find a characterization of what should be their nerves.

    Toby: OK, that fits in with most of what's written here, but not the beginning

    Simplicial models for weak ω\omega-categories – sometimes called simplicial weak ∞-categories – are […] Maybe that was just poorly written, but it threw me off. Should it be A simplicial model for weak ω\omega-categories – which are then sometimes called simplicial weak ∞-categories – is […] or even A simplicial model for weak ω\omega-categories is […] and only later mention simplicial weak ∞-categories?

    Mike: You’re right that ’simplicial ω\omega-category’ it fits into ’globular ω\omega-category’ and ’opetopic ω\omega-category’ and so on. It seems more problematic in this case, though, since simplicial objects of random categories are a good deal more prevalent than globular ones and opetopic ones. But perhaps I should just live with it.

    Urs: I have now expanded the entry text on this point, trying to make very clear to the reader what’s going on here.

    Toby: Thanks, that's much clearer. And if Verity's definition is at weak complicial set, then we may not really need anything at simplicial weak ∞-category, so no need to offend Mike's sensibilities (^_^) either.

    diff, v17, current