Timeline for Is every algebraic space a 1-geometric stack?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2018 at 11:40 | history | edited | Jon Pridham | CC BY-SA 3.0 |
clarified HAG2 references
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| Feb 21, 2018 at 7:56 | comment | added | Jon Pridham | By $\mathrm{map}(S^n,X)$, I just mean the functor $A \mapsto \mathrm{map}(S^n,X(A))$. For set-valued functors $X$, you then have $\mathrm{map}(S^n,X) \simeq X$. | |
| Feb 21, 2018 at 4:40 | comment | added | keaton | On the other hand, why $\mathrm{map}(S^1,X)$ is isomorphic to $X$? | |
| Feb 21, 2018 at 4:29 | comment | added | keaton | Sorry I'm little confusing. What is a definition of $\mathrm{map}(S^n,X)$? I think $X$ lives in the category of functors from $\mathrm{Ho}(sComm)^{op}$ to $\mathrm{SSet}$. Is it make sence to consider a map space from $S^n$ to $X$? | |
| Feb 20, 2018 at 20:50 | history | edited | Jon Pridham | CC BY-SA 3.0 |
added 553 characters in body
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| Feb 20, 2018 at 12:03 | history | edited | Jon Pridham | CC BY-SA 3.0 |
added 261 characters in body
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| Feb 20, 2018 at 10:19 | comment | added | keaton | Thank you. I think you know something and have intuition. Since I'm a just beginner of derived algebraic geometry, I cannot understand that n-geometric is equivalent to that higher diagonal $X \to map(S^n, X)$ is affine. May I ask you the reason why? Is there a theorem saying this in HAG2? | |
| Feb 20, 2018 at 9:11 | history | answered | Jon Pridham | CC BY-SA 3.0 |