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• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeAug 18th 2013

New page: n-types cover

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeAug 18th 2013

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeAug 18th 2013

Thanks! I moved the link to h-set to the section “In homotopy type theory”, and removed the link to suspension since it is not the same as delooping.

• CommentRowNumber4.
• CommentAuthorZhen Lin
• CommentTimeAug 18th 2013

I’ve heard both terms used for the operation $M \mapsto \mathrm{B} M$, where $M$ is a monoidal category and $\mathrm{B} M$ is the corresponding one-object bicategory. (I usually say delooping for that.) Perhaps the difference should be explained somewhere.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeAug 18th 2013
• (edited Aug 18th 2013)

Hm, I don’t remember having linked to suspension

It’s a bad habit of some category theorists to say “suspension” for delooping. A related bad habit is to write $B$ for geometric realization of a category.

While we do have looping and delooping with a fair bit detail, I suppose the entry suspension is lacking some homotopy theoretic discussion. It’s scattered at stable (infinity,1)-category and elsewhere I suppose.

I have no time to do much at all on the nLab right now, though.

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeNov 14th 2014

The page has

By the Kripke-Joyal semantics of homotopy type theory,

following which link we see only

Kripke–Joyal semantics is a natural semantics in a topos.

Presumably the latter should say something about extending to the $\infty$-case.

Maybe first though some detail nees to be given at Kripke-Joyal semantics.

• CommentRowNumber7.
• CommentAuthorMike Shulman
• CommentTimeNov 14th 2014

Yeah…