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12:23 AM
Where can I read a proof that the infinity-category of finite spectra is the stable infinity-category freely generated by an object?
 
12:51 AM
@AlexanderCampbell SAG.C.1.1.7
 
@DylanWilson Excellent, thank you.
 
 
10 hours later…
11:14 AM
What's a simple example of a non-proper map of simplicial sets that still has the property that the pullback of any final map along it is final?
 
 
2 hours later…
1:40 PM
The fact that the Thom spectrum of the J-homomorphism $BU\times Z\to Pic(\mathbb{S})$ can be computed as the Thom spectrum of the map $Z\to Pic(MU)$ that takes $n$ to $\Sigma^{2n}MU$ follows from work of @JonathanBeardsley on relative Thom spectra. Is there a simpler explanation of this case?
 
2:05 PM
@BrunoStonek if you care about the multiplicative structure beyond E_1 then I don't know of another way. If you only care about the E_1-ring structure, then $BU\times \mathbb{Z}$ is the tensor product of $BU$ and $\mathbb{Z}$ in $\mathsf{Alg}_{\mathbb{E}_1}(\mathsf{Spaces}_{/\mathrm{Pic}})$ so you could just use that the Thom spectrum functor is symmetric monoidal to get the formula $MU \wedge S^0[t]$ as $\mathbb{E}_1$-rings (and hence $MU$-modules)
I guess that splitting is probably as E_2 algebras too, but not more than that
 
 
9 hours later…
11:10 PM
👀
 

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