Timeline for The skew monoidal structure induced by a functor
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2018 at 16:28 | comment | added | fosco | Ok, now everything works. | |
| Jul 23, 2018 at 16:14 | comment | added | Giulio Bresciani | I am not sure I understand your question (I am not familiar with the terminology). From what I understand, $\gamma$ is defined as follows: you start from $y\to j^*j_!y$, then $j_!x\circ y\to j_!x\circ j^*j_!y=j^*(j_!x\circ j_!y)$ and finally you get $j_!(j_!x\circ y)\to j_!x\circ j_!y$. Hence, following my terminology above, $\gamma=L\phi$ by definition. | |
| Jul 23, 2018 at 15:45 | comment | added | fosco | There's only a minor detail I don't get: why is the "associator" $\gamma : j_!(j_!x \circ y) \to j_!x\circ j_! y$ in turn obtained mating the unit and the counit of $j_!\dashv j^*$? Once this is clarified, I agree the argument is essentially zig-zag identities for the adjunction. | |
| Jul 23, 2018 at 15:17 | comment | added | fosco | "Faccio geometria, ma sono anche categorista, lo faccio per i soldi" :-) | |
| Jul 23, 2018 at 15:08 | comment | added | Giulio Bresciani | Probably I'm just the first one putting some effort into it: since I don't have much reputation, I needed the bounty for an unanswered question of mine! | |
| Jul 23, 2018 at 15:07 | vote | accept | fosco | ||
| Jul 23, 2018 at 15:05 | history | bounty ended | fosco | ||
| Jul 23, 2018 at 15:04 | comment | added | fosco | I'm actually surprised nobody noticed such a simple argument before! | |
| Jul 23, 2018 at 14:29 | comment | added | Giulio Bresciani | Di nulla! An easy proof just had to exist. I don't even know which are the axioms of a skew monoidal category: sometimes having less information is better. | |
| Jul 23, 2018 at 14:18 | comment | added | fosco | Ah, ho capito qual è l'idea. I was tangled into too many messy diagrams to see this trick. Thx! | |
| Jul 23, 2018 at 14:11 | history | edited | Giulio Bresciani | CC BY-SA 4.0 |
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| Jul 23, 2018 at 13:55 | history | edited | Giulio Bresciani | CC BY-SA 4.0 |
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| Jul 23, 2018 at 13:51 | comment | added | Giulio Bresciani | If someone viewed a previous version of this, it's just because I mistakingly reversed some arrows. With the right direction it's even easier! | |
| Jul 23, 2018 at 13:49 | history | undeleted | Giulio Bresciani | ||
| Jul 23, 2018 at 13:48 | history | edited | Giulio Bresciani | CC BY-SA 4.0 |
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| Jul 23, 2018 at 12:47 | history | deleted | Giulio Bresciani | via Vote | |
| Jul 23, 2018 at 12:42 | history | edited | Giulio Bresciani | CC BY-SA 4.0 |
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| Jul 23, 2018 at 12:07 | history | answered | Giulio Bresciani | CC BY-SA 4.0 |