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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 17th 2012
• (edited May 17th 2012)

I am starting to bring (infinity,n)-category into shape. So far I have

• rewritten the Idea-section

• added a bare minimum of the axiomatic characterization

• also polished n-category a bit.

My plan ist to add now technical details to the entry. Let’s see how far I get.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 17th 2012
• (edited May 17th 2012)

have been further adding material to (infinity,n)-category, mainly such as to give the main statements of the article by Clark Barwick and Chris Schommer-Pries.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 17th 2012

have added more stuff here and there and then had the glorious idea to start a section Web of Quillen equivalent model category presentations.

Just a start, so far. Need a break now.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMay 18th 2012
• (edited May 18th 2012)

have added to the entry further details in “Definition via presentation by strict n-categories” and further properties.

Also wrote sections “Introduction for 1-category theorists” and “Introduction for homotopy theorists”.

I am preparing a seminar talk for an audience of students familiar with, indeed, 1-category theory and homotopy theory. So I’d be interested in how the entry, unfinished as it is, works so far for students with such background.

For instance Stephan? When you are reading this here. Or anyone else, I’d be interested in hearing which points would need more explanation.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 19th 2012
• (edited May 19th 2012)

I have expanded the Idea-section at (infinity,n)-category, mentioning more of the results and applications.

There is more to be done. But I have to interrupt this now and do some string geometry. For a change.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJun 18th 2014

with brief remark and cross-links to some related entries.

• CommentRowNumber7.
• CommentAuthorMike Shulman
• CommentTimeMay 6th 2016

• Rune Haugseng, On the equivalence between $\Theta_n$-spaces and iterated Segal spaces, arXiv

Unfortunately I don’t have time to actually read it or add any substantive remarks to the page.

• CommentRowNumber8.
• CommentAuthorAlexisHazell
• CommentTimeNov 1st 2018

Added reference to Julie Bergner, “A survey of models for (∞,n)-categories”.