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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
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.
I thought we had an entry of the following title
but apparently we do not(?) Will create a stub now…
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?
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.
Is there a simple statement one can make about when $Mon(C)$ models the $\infty$-category of monoids in the $\infty$-category modeled by $C$?
Re #6: Yes, see Theorem 7.11 in https://arxiv.org/abs/1410.5675.
That’s great, I wasn’t aware of this. Let’s record this on some nLab page.
Re #8: Added something here: https://nforum.ncatlab.org/discussion/2124/model-structure-on-algebras-over-an-operad/
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