Timeline for Hammock localization and free adjoints
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 27, 2023 at 20:23 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
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| Sep 25, 2023 at 17:21 | comment | added | Simon Henry | Oh sorry you're right! | |
| Sep 25, 2023 at 17:20 | vote | accept | Simon Henry | ||
| Sep 25, 2023 at 15:37 | comment | added | Dmitri Pavlov | @SimonHenry: If I understood your maps correctly, the vertical morphisms from the first row to the second row would have to include the morphism f, which is not a weak equivalence. For example, in the top row, the first morphism is id:0→0 and in the second row the first morphism is f:0→1, so the first vertical morphism necessarily has to be f:0→1, which is not a weak equivalence and therefore does not yield a legitimate hammock. | |
| Sep 24, 2023 at 23:55 | comment | added | Simon Henry | $0 \rightarrow 0 \leftarrow 0 \rightarrow A \leftarrow F \rightarrow 3$ ? | |
| Sep 24, 2023 at 23:11 | comment | added | Dmitri Pavlov | @SimonHenry: What is the top row? Especially the two leftmost maps. | |
| Sep 24, 2023 at 23:04 | comment | added | Simon Henry | @Dimitri I think These two can be composed. The composite 2-cell has 5 column, with the middle line doing $f: 0 \to 1$, $1 : 1 \leftarrow 1$, $g: 1 \to 2$, $1: 2 \leftarrow 2$ ,$h:2 \to 3$ | |
| Sep 24, 2023 at 20:57 | comment | added | Dmitri Pavlov | @SimonHenry: I fixed the second hammock by adding another zigzag. | |
| Sep 24, 2023 at 20:56 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
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| Sep 24, 2023 at 19:36 | comment | added | Simon Henry | Ok, after more thought, I don't think that example works and I don't immediately see how to fix it (every time I replace the second thing by a Hammock I get a composition), but I'm starting to feel like the uniqueness of composition might fail in some cases and hence that you're general point is probably valid - I need to think more about this! | |
| Sep 24, 2023 at 18:39 | comment | added | Simon Henry | Thanks, I'll need a bit of time to digest this completely, but just reading it, I'm confused by something: The second hammock seems like it is not a hammock, it has two successive column going to the right (the definition of Hammock impose that adjacent column go in opposite direction). It is not super clearly said in the nLab page, but this is very explicit in Dwyer and Kan's paper. Anyway, I'll go think about this more... | |
| Sep 24, 2023 at 16:43 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |