Timeline for A question about rigid objects in monoidal categories
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
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| Jan 10 at 17:42 | history | edited | Yilmaz Caddesi | CC BY-SA 4.0 |
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| Nov 29, 2023 at 15:16 | comment | added | Martin Brandenburg | Maybe remove the false claim in your question? (It clearly doesn't hold for all isomorphisms, just consider $\lambda \cdot f_r$ for example.) | |
| Nov 25, 2023 at 13:17 | vote | accept | Yilmaz Caddesi | ||
| Nov 25, 2023 at 3:16 | answer | added | Sebastien Palcoux | timeline score: 4 | |
| Nov 24, 2023 at 22:59 | comment | added | Yilmaz Caddesi | If somebody would like to present this discussion as a formal answer, then I would be happy to accept it. | |
| Nov 24, 2023 at 22:01 | comment | added | Yilmaz Caddesi | Ok, thanks for the links! | |
| Nov 24, 2023 at 16:45 | comment | added | Sebastien Palcoux | It is almost immediate using graphical calculus, so you need to learn that. You can read Sections 2 and 7 of my paper arxiv.org/abs/2203.06522 or watch my course of current semester on YouTube, from Session 3 at 15:00, youtu.be/zJvNsVUybKE ; and from Session 10 at 43:00 youtu.be/98lkVDT7hIo | |
| Nov 24, 2023 at 15:42 | history | edited | Yilmaz Caddesi | CC BY-SA 4.0 |
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| Nov 24, 2023 at 15:37 | comment | added | Yilmaz Caddesi | @Sebastien Palcoux: thanks a lot for comment. Could you explain this in more detail? | |
| Nov 24, 2023 at 15:28 | history | edited | Yilmaz Caddesi | CC BY-SA 4.0 |
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| Nov 24, 2023 at 14:12 | comment | added | Sebastien Palcoux | Using the definition of evaluation and coevaluation maps (zigzag relations), your first identity is equivalent to $f_r^* = f_l$. | |
| Nov 24, 2023 at 13:59 | comment | added | Sebastien Palcoux | There are at least two $M$ which should be $\mathcal{A}$, and for the second identity you should swap the composition for making sense, and then it is not a morphism from $M \otimes M$, but you should put appropriate dual. | |
| Nov 24, 2023 at 13:55 | comment | added | Yilmaz Caddesi | @Adrien: What kind of relationship between $f_l$ and $f_r$ are you suggesting? Also thank you for suggestion about graphical calculus! | |
| Nov 24, 2023 at 13:49 | comment | added | Adrien | Do you have any relation between $f_l$ and $f_r$ ? Otherwise it's clearly wrong (also for f.d. vector spaces), unless I'm missing something. Then this is typically the sort of questions where you want to use graphical calculus (if you're a newcomer in the world of rigid monoidal categories and haven't heard of graphical calculus yet, I strongly suggest you look it up !) | |
| Nov 24, 2023 at 13:38 | history | edited | Yilmaz Caddesi | CC BY-SA 4.0 |
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| Nov 24, 2023 at 13:38 | comment | added | Yilmaz Caddesi | Good point! I will fix it. | |
| Nov 24, 2023 at 13:36 | comment | added | Sebastien Palcoux | The notation $M$ cannot be used for both the object and the category. | |
| Nov 24, 2023 at 13:33 | comment | added | Yilmaz Caddesi | @SebastienPalcoux: Thanks you for seeing the typos! I have tried to fix them all and to specify the objects for $\epsilon$ and $\eta$. | |
| Nov 24, 2023 at 13:32 | history | edited | Yilmaz Caddesi | CC BY-SA 4.0 |
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| Nov 24, 2023 at 13:18 | history | edited | Yilmaz Caddesi | CC BY-SA 4.0 |
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| Nov 24, 2023 at 3:29 | comment | added | Sebastien Palcoux | I guess you swapped X and M. Not evolution but evaluation. What is $f$? Can you specify the object for every morphism ($\mathrm{id}$, $\eta$, $\epsilon$)? | |
| S Nov 23, 2023 at 16:10 | review | First questions | |||
| Nov 23, 2023 at 16:12 | |||||
| S Nov 23, 2023 at 16:10 | history | asked | Yilmaz Caddesi | CC BY-SA 4.0 |