Timeline for Realization of a constant simplicial anima
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7 at 9:17 | comment | added | Achim Krause | AH, I think I know what's going on: When they write $\mathrm{const}_1(\mathcal{C})$, they don't mean your $\mathrm{const}_1$, instead they mean the simplicial diagram left Kan extended from the functor $\Delta_{\leq 1}\to \mathrm{Cat}$ taking $[0]\mapsto 0$ and $[1]\mapsto \mathcal{C}$. This should realize to the suspension of $\mathcal{C}^\simeq$, and a map $\Sigma\mathcal{C}^\simeq \to |Q(\mathcal{C})|$ corresponds to a map $\mathcal{C}^\simeq \to \Omega|Q(\mathcal{C})|$ by adjunction. | |
| Aug 7 at 1:49 | vote | accept | XiaYu | ||
| Aug 7 at 1:39 | comment | added | XiaYu | And I totally agree with you that this shouldn't be a equivalence. | |
| Aug 7 at 1:35 | comment | added | XiaYu | Thanks for your answer. In 4.1.27 $const_1(C)\rightarrow Q(C)$ only implies $|const_1(C^{\simeq})|\rightarrow |Q(C)^{\simeq}|$, but $K(C)=\Omega |Q(C)^{\simeq}|$(as in definition 4.1.24) so it seems that there may be some natural morphism $C^{\simeq}\rightarrow \Omega|const_1(C^{\simeq})|$. That's why I expected something about $\Omega|const_1(C^{\simeq})|$ to be told. | |
| Aug 6 at 13:23 | history | answered | Achim Krause | CC BY-SA 4.0 |