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I added the comment
Equivalently, a symmetric monoidal (∞,1)-category is a commutative algebra in an (infinity,1)-category in the (infinity,1)-category of (infinity,1)-categories.
to the introduction of symmetric monoidal (infinity,1)-category. I hope that’s correct…
I also added the reference
(and also to E-infinity-ring).
Also noticed that we have two different pages commutative ring spectrum and E-infinity-ring…
Here the idea should be that the former entry is more about the models, whereas the latter is about the general infty-categorical concept. But if itdoes ot work out of course the we might want to merge them.
(I guess you mean the other way around.) So commutative algebra in an (infinity,1)-category is the general concept, and E-infinity ring is the special case where the (infinity,1)-category is Spt = Stab(Spc). Should commutative ring spectrum be something in the middle, e.g. commutative algebra objects in the stabilization of some (infinity,1)-category, maybe?
added pointer to
both to symmetric monoidal (infinity,1)-category and to monoidal model category.
I am quoting the page
This can be understood as a special case of an (∞,1)-operad (…to be expanded on…)
Did anyone ever get round to adding this?
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