Timeline for Long exact sequences for parametrized cohomology
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2022 at 13:46 | comment | added | Marc Hoyois | "Higher topos theory" by Lurie is the standard reference for $\infty$-topoi. Although in this case the appeal to "descent" is maybe overkill, we only really use the universal property of the pushout in the slice category $T_{/D}$ to write a mapping space out of $D$ as a pullback of mapping spaces. As for the fact that a cartesian square of pointed types induces a long exact sequence, I don't know a reference, but the trick is that such a cartesian square $(X,Y)\Rightarrow(Z,W)$ induces a fiber sequence $\Omega W\to X \to Y\times Z$, whence a long exact sequence. | |
| Aug 29, 2022 at 11:35 | comment | added | ಠ_ಠ | Beautiful! Getting the long exact sequence for pushout squares is even better than I expected. Are there any sources that you would recommend for more of the details here? I'm reasonably comfortable with HoTT and I know that HoTT is supposed to be the internal language of infinity-topoi, but I don't know any infinity topos theory itself (e.g. slice infinity-topoi, descent etc.). | |
| Aug 29, 2022 at 11:21 | vote | accept | ಠ_ಠ | ||
| Aug 29, 2022 at 9:02 | history | edited | Marc Hoyois | CC BY-SA 4.0 |
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| Aug 29, 2022 at 5:48 | history | answered | Marc Hoyois | CC BY-SA 4.0 |