Timeline for Corepresentability of involutory objects in monoidal $\infty$-categories
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2021 at 21:02 | vote | accept | Emily | ||
| Sep 19, 2021 at 21:02 | history | edited | Emily | CC BY-SA 4.0 |
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| Sep 19, 2021 at 11:26 | comment | added | Dylan Wilson | (Re the original question): Couldn't I take the pushout in E_k-spaces of pt<---Free(x)--->Free(y) where x goes to y^2? | |
| Sep 19, 2021 at 11:13 | answer | added | Maxime Ramzi | timeline score: 4 | |
| Sep 19, 2021 at 10:56 | comment | added | Maxime Ramzi | Also, the lifting of $Inv$ to $Ab$ makes $\mathbb Z/2$ into a co-abelian group in $CMon$ - which is not a surprise, everyone is a co-(commutative monoid) in $CMon$, and the corresponding shear map is just the shear map | |
| Sep 19, 2021 at 10:52 | comment | added | Maxime Ramzi | I think if $C$ is $E_k$-monoidal and $X$ is $E_1$-monoidal, then $Fun^\otimes(X,C)$ is $E_{k-1}$-monoidal, not $E_1$-monoidal (think of $k=1$: what is a monoidal structure on $Fun^\otimes(C,D)$ for $C,D$ barely monoidal ? on $Alg(D)$ ? ); the case of $X=\mathbb Z$ is special, because $Fun^\otimes(\mathbb Z,C)\to C$ is the inclusion of a full sub-groupoid which is stable under tensor products. Your question still makes sense though, if you replace the second $E_k$ with an $E_{k-1}$ | |
| Sep 19, 2021 at 4:47 | history | edited | Emily | CC BY-SA 4.0 |
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| Sep 19, 2021 at 1:32 | history | edited | Emily | CC BY-SA 4.0 |
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| Sep 18, 2021 at 23:34 | history | edited | Emily | CC BY-SA 4.0 |
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| Sep 18, 2021 at 22:26 | history | edited | Emily | CC BY-SA 4.0 |
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| Sep 18, 2021 at 19:57 | history | asked | Emily | CC BY-SA 4.0 |