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-categories 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-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry 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 homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories 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 stack 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
    • CommentTimeMay 21st 2012
    • (edited May 21st 2012)

    I have moved a Properties-section to strict n-category, taken from (infinity,n)-category (where it serves as a preliminary), which collects the statements from section 2 of Barwick&Schommer-Pries (see the refereces there).

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeMay 21st 2012

    I see that they define a suspension of nn-category as certain n+1n+1-category with 2 objects. But the tradition (especially used by Baez) is that one calls suspension of CC as the n+1n+1-category with only one object and with CC-worth of endomorphisms of that object. Why the change of terminology is warranted ? Any comments ?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 21st 2012

    It’s just a word. Feel free to invent another word.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeMay 21st 2012

    So what will be your usage – which one will you call a suspension ?

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeMay 21st 2012

    IMHO what you call the “traditional” usage is wrong. It only make sense when CC is monoidal, and according to the topological analogy, that construction should really be called the delooping. Delooping and suspension are equivalent in the stable world (spectra) but not in the unstable world. This point confused me for a while when I was first learning about higher categories, so I think we should eschew the use of “suspension” to mean “delooping”. The B-CP usage of “suspension” is better.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 21st 2012

    If I had written that article I had tried to find some different word, to avoid overuse.

    But I don’t think it matters since this word is not going to be used broadly, it’s just some word for convenience in those paragraphs where it appears. You can just call it “σ\sigma”. Or anything else. :-)

    • CommentRowNumber7.
    • CommentAuthorzskoda
    • CommentTimeMay 21st 2012

    Mike, that is about discussion which I was seeking for. Thanks, Urs, as well.

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)