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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 10th 2015
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   Author: Urs
   Format: MarkdownItexWhen somebody asked me about the sSet enrichment of cosimplicial objects, I noticed that the nLab didn't have the pointers. So I have now split off a stub _[[cosimplicial object]]_ from _[[simplicial object]]_ and added a bare minimum of pointers. No time for more at the moment.

   When somebody asked me about the sSet enrichment of cosimplicial objects, I noticed that the nLab didn’t have the pointers. So I have now split off a stub cosimplicial object from simplicial object and added a bare minimum of pointers. No time for more at the moment.

2. • CommentRowNumber2.
   • CommentAuthorZhen Lin
   • CommentTimeFeb 10th 2015
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   Author: Zhen Lin
   Format: MarkdownItexThere is no need to assume finite limits or colimits. I added an end formula for the hom-spaces: in effect, all we are doing is forming the totalisation of the cosimplicial simplicial set $\mathcal{C} (X^{\bullet}, Y^{\bullet})$.

   There is no need to assume finite limits or colimits. I added an end formula for the hom-spaces: in effect, all we are doing is forming the totalisation of the cosimplicial simplicial set $\mathcal{C} (X^{\bullet}, Y^{\bullet})$.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 10th 2015
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   Author: Urs
   Format: MarkdownItexThanks!

   Thanks!

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 10th 2015
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   Author: Urs
   Format: MarkdownItexActually, the question was about the simplicial tensoring.

   Actually, the question was about the simplicial tensoring.

5. • CommentRowNumber5.
   • CommentAuthorZhen Lin
   • CommentTimeFeb 10th 2015
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   Author: Zhen Lin
   Format: MarkdownItexAh. Then you will need colimits in $\mathcal{C}$.

   Ah. Then you will need colimits in $\mathcal{C}$.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeFeb 10th 2015
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   Author: Urs
   Format: MarkdownItexI should have said it here as I did say it in the entry: what is called the "external simplicial structure" in [Quillen 67](http://ncatlab.org/nlab/show/cosimplicial%20object#Quillen67), recalled for instance as [Bousfield 03, section 2.10](http://ncatlab.org/nlab/show/cosimplicial%20object#Bousfield03) involves the enrichment, the powering and the tensoring. That's what I was pointing to. But I should have said so more clearly.

   I should have said it here as I did say it in the entry: what is called the “external simplicial structure” in Quillen 67, recalled for instance as Bousfield 03, section 2.10 involves the enrichment, the powering and the tensoring. That’s what I was pointing to. But I should have said so more clearly.