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3:51 PM
Let's say I have a small category $A$. Does there in general exist a right Bousfield localisation of simplicial presheaves on $A$ with the injective model strucure, where the weak equivalences are created by homotopy limits? What if I make extra assumptions, such as $A$ having a contractible classifying space or being a test category?
 
 
1 hour later…
5:18 PM
'sometimes'
The problem with right-bousfield localizations is that presentable ∞-categories aer an inherently handed-notion
 
 
5 hours later…
10:14 PM
lol okay trying to fix some silly paper of mine about ∞-categories and it's been quite a while since I've thought about this type of thing... in Lurie's framework, "lax monoidal" is a map of ∞-operads between monoidal ∞-categories right?
 
10:37 PM
It's a relative operad map over Assoc.
if you did it over Fin_* you get lax symm monoidal.
 
10:51 PM
Yeah right okay... by defining algebras as sections that preserve the inert morphisms, an ∞-operad map, which preserves inert morphisms by definition, necessarily takes algebras to algebras...
 

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