Timeline for Why are $G$-Extensions of fusion categories rigid, when constructed via monoidal 2-functors $G \to \underline{\underline{BrPic}}(\mathcal{D})$?
Current License: CC BY-SA 4.0
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| Jul 1, 2021 at 17:38 | comment | added | Noah Snyder | You use invertibility to identify $C_e$ with A-mod-A. Without invertibility you’re right you couldn’t get an action in the other side. | |
| Jul 1, 2021 at 16:10 | comment | added | Nicolas Cage | Thinking about it again that wouldn't work, because the left and right action wouldn't commute. | |
| Jul 1, 2021 at 16:03 | comment | added | Nicolas Cage | Thanks, that clears things up! When you identify $C_g$ with $A$-mod, how do you get the $C_e$-left module structure on $C_g$? I guess it should be something like $c \in C$ acting from the left as $c^*$ from the right (using rigidity of $C$). But that would require an identification of $C_g$ with $C_g^{op}$. These two categories are equivalent but not canonically, so I guess it would boil down to an arbitrary choice of non-degenerate trace on each $C_g$? | |
| Jun 30, 2021 at 21:35 | vote | accept | Nicolas Cage | ||
| Jun 30, 2021 at 19:24 | history | edited | Noah Snyder | CC BY-SA 4.0 |
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| Jun 30, 2021 at 19:02 | history | edited | Noah Snyder | CC BY-SA 4.0 |
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| Jun 30, 2021 at 18:56 | comment | added | Noah Snyder | I should say the info from the first paragraph came from Dmitri and Victor when I emailed them this exact question a month ago. | |
| Jun 30, 2021 at 18:53 | history | answered | Noah Snyder | CC BY-SA 4.0 |