Timeline for This is not a tensor: tensoring abelian groups over groups
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 22, 2021 at 5:40 | comment | added | Emily | ï¼ AlexanderCampbell Thanks! | |
| Oct 21, 2021 at 20:26 | history | edited | Alexander Campbell | CC BY-SA 4.0 |
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| Oct 21, 2021 at 20:25 | comment | added | Alexander Campbell | @Emily Oops, that isomorphism is not correct, I don't know why I wrote that. Let me correct my answer. | |
| Oct 21, 2021 at 20:07 | comment | added | Emily | Incidentally, do you know if the isomorphism $X\odot G\cong G\times F(X)$ (is there a 'slick proof' of it?) generalises to give a tensoring of $E_n$-monoids by $E_{k}$-monoids for $k\leq n-1$, via $X\odot Y\cong Y\times\mathsf{Free}_{\mathbb{E}_{k},\mathbb{E}_n}(X)$? (So e.g., there being a tensor of braided monoidal categories by monoidal categories via $\mathcal{C}\odot\mathcal{D}\cong\mathcal{D}\times \mathsf{Free}_{\mathsf{mon},\mathsf{br}\text{-}\mathsf{mon}}(\mathcal{C})$) | |
| Oct 21, 2021 at 20:07 | comment | added | Emily | Hi Alexander! Thank you very much, this is really wonderful! (I was a bit disappointed thinking that we'd probably have to work with some variant of lax monoidal categories for this to work, but your answer convinced me that this is definitely the natural thing to do in this case! :) | |
| Oct 21, 2021 at 20:07 | vote | accept | Emily | ||
| Oct 21, 2021 at 1:30 | history | edited | Alexander Campbell | CC BY-SA 4.0 |
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| Oct 21, 2021 at 1:22 | history | answered | Alexander Campbell | CC BY-SA 4.0 |