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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeSep 8th 2011
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   Author: Mike Shulman
   Format: MarkdownItexCreated [[saturated class of limits]].

   Created saturated class of limits.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeFeb 22nd 2012
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   Author: Mike Shulman
   Format: MarkdownItexI've corrected an error (which I think I introduced myself) at [[saturated class of limits]] and also at [[finite limit]], which claimed that the class of finite limits is saturated. This is false. For instance, the quotient of an object by a $\mathbb{Z}$-action clearly lies in this saturation (it is the coequalizer of the action of $1\in \mathbb{Z}$ and the identity), but it is not a finite limit. The actual answer, I believe, is that the saturation of finite limits (and hence also the saturation of finite products with equalizers, and the saturation of pullbacks with a terminal object) is the class of [[L-finite limits]]. I also added some remarks at [[saturated class of limits]] about conical limits in the $Set$-enriched case, for which the open question is known to be true.

   I’ve corrected an error (which I think I introduced myself) at saturated class of limits and also at finite limit, which claimed that the class of finite limits is saturated. This is false. For instance, the quotient of an object by a $\mathbb{Z}$-action clearly lies in this saturation (it is the coequalizer of the action of $1\in \mathbb{Z}$ and the identity), but it is not a finite limit. The actual answer, I believe, is that the saturation of finite limits (and hence also the saturation of finite products with equalizers, and the saturation of pullbacks with a terminal object) is the class of L-finite limits.

   I also added some remarks at saturated class of limits about conical limits in the $Set$-enriched case, for which the open question is known to be true.