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12:43 PM
Does anyone know where I can find an explicit description of a cofibrant dendroidal set/segal-space modeling the terminal infinity operad?
 
 
5 hours later…
5:43 PM
@DenisNardin a while back we were talking about the G-category $Fin_G$ of finite G-sets, and you suggested that at least when G is abelian, the $W(H)$-action on $(Fin_G)^H := (Fin^G)_{/(G/H)}$ should be trivial. is it possible that in fact $Fin_G$ is simply the unstraightening of the functor
$$ O_G \to P_G \to Grp \xrightarrow{B} Gpds \xrightarrow{Fun(-,Fin)} Cat^{op} ~ ? $$
here, $P_G$ is the poset of subgroups of $G$ as they're related by subconjugacy, and the special thing about G being abelian is that there's a functor from this to Grp (in fact to $Grp_{/G}$).
(of course i'd be happy to hear from anyone on this, i'm just pinging denis since the two of us were discussing this a while back.)
@blank_space i'd be genuinely happy to hear from you. if you write me a book, i'll read it.
and i'm really sorry for the gaslighting. i know how frustrating it can be, especially after having shared vulnerably.
 
6:39 PM
@AaronMazel-Gee I'm pretty sure it's true, and in any case, a "simpler" formulation is X maps to Fun(X/G,Fin) I guess.
So that it is easily seen to be a functor from the span category of the orbits, I guess?
 
 
1 hour later…
7:44 PM
Presumably we have homomorphisms $\mathrm{Aut}(\mathbb{E}_m)\times \mathrm{Aut}(\mathbb{E}_n) \to \mathrm{Aut}(\mathbb{E}_m\otimes \mathbb{E}_n) \approx \mathrm{Aut}(\mathbb{E}_{m+n})$. So it seems like $\{\mathrm{Aut}(\mathbb{E}_n)\}$ is yet another series of groups which behaves like $\{O(n)\}$ or $\{\mathrm{Top}(n)\}$.
 

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