Timeline for Group objects in $\infty$-categories
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Oct 17, 2022 at 9:51 | history | suggested | Ken | CC BY-SA 4.0 |
fixed the mistakes pointed out in the comment
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| Oct 17, 2022 at 6:31 | review | Suggested edits | |||
| S Oct 17, 2022 at 9:51 | |||||
| Feb 24, 2018 at 14:26 | comment | added | Dylan Wilson | The functor is monoidal (not just lax monoidal) for the ‘concatenate’ monoidal structure on the source. But it is also more than that because we’re allowed to decompose in more general ways | |
| Feb 24, 2018 at 0:02 | comment | added | Exit path | @DylanWilson Yes I do mean $\Delta$ and 'final object,' thanks. That makes sense. Is it easy to see as well that the functor is lax monoidal, if the monoidal structure is given by products? | |
| Feb 24, 2018 at 0:02 | comment | added | Dylan Wilson | (If you're familiar with the 'Kan complexes are $\infty$-groupoids' point of view, then this `decomposition--> pullback' condition is equivalent to having fillers for all horns. See, e.g. HTT.6.1.2.6) | |
| Feb 24, 2018 at 0:00 | comment | added | Dylan Wilson | I think you mean $\Delta$ instead of finite sets, and 'contractible' maybe means 'final object'. Use the decomposition $[2] = \{0,1\} \cup \{0,2\}$ and then lift the pair $(x,e)$ to something in $G^{\times 2}$, $(x,y)$. By definition, $xy = e$, and there's your inverse. | |
| Feb 23, 2018 at 22:41 | history | asked | Exit path | CC BY-SA 3.0 |