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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeDec 12th 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI 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.

   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.

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeDec 12th 2011
   • (edited Dec 13th 2011)
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexNot 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?

   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?

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeDec 13th 2011
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   Author: Mike Shulman
   Format: MarkdownItex> 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.

   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.

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeDec 13th 2011
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   Author: TobyBartels
   Format: MarkdownItexAh, 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.

   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.