Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 21st 2012
   • (edited May 21st 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI 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).

   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).

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeMay 21st 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI see that they define a suspension of $n$-category as certain $n+1$-category with 2 objects. But the tradition (especially used by Baez) is that one calls suspension of $C$ as the $n+1$-category with only one object and with $C$-worth of endomorphisms of that object. Why the change of terminology is warranted ? Any comments ?

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

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 21st 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexIt's just a word. Feel free to invent another word.

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

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeMay 21st 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexSo what will be _your_ usage -- which one will you call a suspension ?

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

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeMay 21st 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexIMHO what you call the "traditional" usage is wrong. It only make sense when $C$ 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.

   IMHO what you call the “traditional” usage is wrong. It only make sense when $C$ 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.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMay 21st 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexIf 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 "$\sigma$". Or anything else. :-)

   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 “$\sigma$”. Or anything else. :-)

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeMay 21st 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexMike, that is about discussion which I was seeking for. Thanks, Urs, as well.

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

8. • CommentRowNumber8.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 15th 2019
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexDeleted the redirects for strict ∞-categories, since these already direct to [[strict omega-category]]. <a href="https://ncatlab.org/nlab/revision/diff/strict+n-category/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/strict+n-category/9">v9</a>, <a href="https://ncatlab.org/nlab/show/strict+n-category">current</a>

   Deleted the redirects for strict ∞-categories, since these already direct to strict omega-category.

   diff, v9, current

9. • CommentRowNumber9.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 15th 2019
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexDeleted the redirects for strict ∞-categories, since these already direct to [[strict omega-category]]. <a href="https://ncatlab.org/nlab/revision/diff/strict+n-category/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/strict+n-category/10">v10</a>, <a href="https://ncatlab.org/nlab/show/strict+n-category">current</a>

   Deleted the redirects for strict ∞-categories, since these already direct to strict omega-category.

   diff, v10, current