Timeline for Showing left module actions are highly structured
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2015 at 19:49 | comment | added | Jonathan Beardsley | It seems that 4.4.2.10 of Higher Algebra gives some sort of handle on this kind of thing. | |
| Feb 3, 2015 at 19:48 | comment | added | Jonathan Beardsley | @RuneHaugseng Yeah, definitely. We fleshed this out a little bit more in the chat room (we being Saul and I). I guess the idea is that you've got all the edges and you know the diagrams commute "up to homotopy" but you don't have all the higher structure. | |
| Feb 3, 2015 at 17:47 | comment | added | Rune Haugseng | It's not entirely clear to me what you're asking, but if you have a map $a : R \otimes M \to M$ and want to turn it into an $R$-module then you still have an infinite amount of data left to specify: first you want a homotopy between the two maps $R \otimes R \otimes M \to M$ given by "apply $a$ twice" and "multiply and then apply $a$", and then similar things with more $R$s. (In an ordinary category these are just properties of the map $a$, but for $\infty$-categories they are extra data.) I expect you're well aware of this and are actually asking about something else, though! | |
| Feb 3, 2015 at 16:49 | answer | added | David White | timeline score: 1 | |
| Feb 3, 2015 at 2:56 | history | edited | Jonathan Beardsley | CC BY-SA 3.0 |
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| Feb 3, 2015 at 2:40 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |