Timeline for A question about possibly $\infty$-category or functors
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 27, 2021 at 16:37 | vote | accept | Ho Man-Ho | ||
| Aug 27, 2021 at 16:07 | answer | added | Dmitri Pavlov | timeline score: 2 | |
| Aug 27, 2021 at 15:59 | comment | added | Ho Man-Ho | @AchimKrause If I say for any two manifolds M and N and a smooth map $f:N\to M$ (which is a morphism), $\Omega(f):\Omega(M)\to\Omega(N)$ is the pullback of forms, does it make sense? | |
| Aug 27, 2021 at 15:55 | comment | added | Achim Krause | Superficially, it looks like you want a natural transformation between functors $\operatorname{Man} \to \operatorname{Cat}$. However, for that to make sense, you need to make sense of $\Omega(M)$ as a category, and pointwise $T(M): \operatorname{Vect}_\Delta(M) \to \Omega(M)$ as a functor of categories. | |
| Aug 27, 2021 at 15:36 | history | edited | Ho Man-Ho | CC BY-SA 4.0 |
Thanks to AT0 for correcting a mistake.
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| Aug 27, 2021 at 15:31 | comment | added | Ho Man-Ho | I am probably wrong. In principle $\Omega^*:\textrm{Man}^{\textrm{op}}\to\textrm{Set}$ should be a functor to the category of sets. I will revise my question. Thank you. | |
| Aug 27, 2021 at 13:29 | comment | added | AT0 | I dont understand what is 'the category of differential forms on M', what category structure are you considering? | |
| Aug 27, 2021 at 12:38 | history | edited | Ho Man-Ho | CC BY-SA 4.0 |
added 2 characters in body
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| Aug 27, 2021 at 12:35 | comment | added | Ho Man-Ho | Thanks, I will check if 2-categories suffice | |
| Aug 27, 2021 at 11:10 | comment | added | Fernando Muro | I think 2-categories would suffice here, but I may be wrong | |
| Aug 27, 2021 at 9:48 | history | asked | Ho Man-Ho | CC BY-SA 4.0 |