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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 18th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[model structure on monoids in a monoidal model category]], for the moment only to host Schwede-Shipley's lemma on homotopy pushouts along free monoid morphisms

   stub for model structure on monoids in a monoidal model category, for the moment only to host Schwede-Shipley’s lemma on homotopy pushouts along free monoid morphisms

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 18th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the statements of the existence results by Schwede-Shipley and by Berger-Moerdijk. Also added a sketch of the proof of some statements about homotopy pushouts.

   added the statements of the existence results by Schwede-Shipley and by Berger-Moerdijk. Also added a sketch of the proof of some statements about homotopy pushouts.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 29th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexI thought we had an entry of the following title * [[model structure on modules in a monoidal model category]] but apparently we do not(?) Will create a stub now... <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+monoids+in+a+monoidal+model+category/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+monoids+in+a+monoidal+model+category/10">v10</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+monoids+in+a+monoidal+model+category">current</a>

   I thought we had an entry of the following title

   • model structure on modules in a monoidal model category

   but apparently we do not(?) Will create a stub now…

   diff, v10, current

4. • CommentRowNumber4.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMay 29th 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexThe article [[model structure on monoids in a monoidal model category]] has a lot of overlap with [[monoid axiom]]. Since the latter was introduced for the specific purpose of the former, do we really need two articles?

   The article model structure on monoids in a monoidal model category has a lot of overlap with monoid axiom.

   Since the latter was introduced for the specific purpose of the former, do we really need two articles?

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 30th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexWhat do you imagine would be gained by merging the entries? It seems to me that the moment somebody starts adding more examples and applications of model structures on monoids, they would have to be split again.

   What do you imagine would be gained by merging the entries?

   It seems to me that the moment somebody starts adding more examples and applications of model structures on monoids, they would have to be split again.

6. • CommentRowNumber6.
   • CommentAuthorHurkyl
   • CommentTimeAug 10th 2022
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexIs there a simple statement one can make about when $Mon(C)$ models the $\infty$-category of monoids in the $\infty$-category modeled by $C$?

   Is there a simple statement one can make about when $Mon(C)$ models the $\infty$-category of monoids in the $\infty$-category modeled by $C$?

7. • CommentRowNumber7.
   • CommentAuthorDmitri Pavlov
   • CommentTimeAug 10th 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexRe #6: Yes, see Theorem 7.11 in <https://arxiv.org/abs/1410.5675>.

   Re #6: Yes, see Theorem 7.11 in https://arxiv.org/abs/1410.5675.

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeAug 10th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexThat's great, I wasn't aware of this. Let's record this on some nLab page.

   That’s great, I wasn’t aware of this. Let’s record this on some nLab page.

9. • CommentRowNumber9.
   • CommentAuthorDmitri Pavlov
   • CommentTimeAug 10th 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexRe #8: Added something here: <https://nforum.ncatlab.org/discussion/2124/model-structure-on-algebras-over-an-operad/>

   Re #8: Added something here: https://nforum.ncatlab.org/discussion/2124/model-structure-on-algebras-over-an-operad/