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• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeDec 12th 2011

I figured it was high time we had a general page on truncated objects. I think some number of links, and perhaps redirects, which currently point to n-truncated object of an (infinity,1)-category would more usefully point here, but I haven’t updated any yet.

• CommentRowNumber2.
• CommentAuthorTobyBartels
• CommentTimeDec 12th 2011
• (edited Dec 13th 2011)

Not only a number of links and redirects, but the redirect created by your link in this very forum discussion! I was going to clear it, but then I figured that I’d move more redirects, and then I realised that I have absolutely no idea what the difference is supposed to be between these two pages. Isn’t a truncated object necessarily an n-truncated object of an (infinity,1)-category for some $n$ and some $(\infty,1)$-category?

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeDec 13th 2011

Isn’t a truncated object necessarily an n-truncated object of an (infinity,1)-category for some n and some (∞,1)-category?

Well, interpreting that statement literally, it is true, but it’s not true that for a given $n$-category $C$ the notion of $k$-truncated object in $C$ coincides with the notion of $m$-truncated object in any $(\infty,1)$-category. If $k$ is of the form $(k,0)$ then it is true – we can take the underlying $(n,1)$-category of $C$ and regard it as an $(\infty,1)$-category. But the underlying $(2,1)$-category of a 2-category doesn’t see the difference between 1-truncated and (1,0)-truncated objects.

Personally, I would suggest we link to n-truncated object of an (infinity,1)-category when the reference is specifically to $(\infty,1)$-categories, and to truncated object if not.

• CommentRowNumber4.
• CommentAuthorTobyBartels
• CommentTimeDec 13th 2011

Ah, I see now! Your article is about $(\infty,\infty)$-categories, while Urs’s is about $(\infty,1)$-categories (although maybe it’s unfair to ascribe the articles to people in this way). As your topic is more general, most redirects should go to your article by default, even if links might go to Urs’s. I have done this.