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Martin Sleziak
Martin Sleziak
5:53 AM
in MO editors' lounge, 1 min ago, by Martin Sleziak
Perhaps somebody knowledgeable in algebraic topology could check whether this edit changing "(S^2) v (S^3)" to "$S^2\times S^3$" at the end of the first paragraph was correct or whether it changed meaning of the post. The relevant part now reads: "to the $4$-skeleton of $S^2\times S^3$, which is $S^2\times S^3$".
 
 
4 hours later…
Bruno Stonek
Bruno Stonek
10:01 AM
@MikeMiller @DenisNardin that does it. thanks a bunch!
 
 
4 hours later…
Omar Antolín-Camarena
Omar Antolín-Camarena
2:21 PM
@MartinSleziak You're right. I changed it to $S^2 \vee S^3$.
 
Martin Sleziak
Martin Sleziak
@OmarAntolín-Camarena Thanks for doing that. (it's strange that none of the reviewers noticed that. I was a bit hesitant to edit myself, since it's not a topic I am familiar with.)
 
 
2 hours later…
nikitas
nikitas
4:19 PM
@DenisNardin thanks for the reference ! I was hoping to avoid the infinity category stuff though...
 
Denis Nardin
Denis Nardin
Well, that is mainly for the definition. But the problem is that the Burnside category is genuinely ∞, that is there are nontrivial homotopies. If you prefer you can use topologically enriched categories, like Guillou and May, but I always found that model cumbersome. If you are interested only in the homotopy category though that is very easy to describe: it is just the span category of finite G-sets
 
Bogdan
Bogdan
4:50 PM
Does localizing a stable (symmetric monoidal) oo-cat with respect to a subcategory that is a tensor ideal preserve algebras over any operad ? How do you see it ?
I am aware of Hill-Hopkins, where they only require the localizing subcategory to be closed under tensor, but there is a condition on the operad. I think the claim above is easier to see
 

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