Timeline for Does inclusion from n-stacks into (n+1)-stacks preserve the sheaf condition?
Current License: CC BY-SA 4.0
7 events
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| Apr 8, 2021 at 2:09 | comment | added | Dan Petersen | Yes David, you've got it exactly. So the point is that $\pi_0$ is a left adjoint unstably, but stably it is the composition of two truncation functors, one which kills positive degrees (and is a left adjoint) and another which kills negative degrees (and is a right adjoint). | |
| Apr 7, 2021 at 23:54 | comment | added | Dmitri Pavlov | @DavidCorwin: The inclusion (if you can call it that) of sets into spectra does not preserve homotopy limits. The inclusion of spaces into spectra also does not preserve homotopy limits. | |
| Apr 7, 2021 at 21:34 | comment | added | David Corwin | So does the inclusion from sets into spectra not preserve limits, even though the inclusion from sets into spaces does? | |
| Apr 7, 2021 at 21:34 | comment | added | David Corwin | To clarify, I meant that my question was why one of those functors preserves limits and the other doesn't. Anyway, it seems that the answer is simply that one consists only of connective objects while the other is stable! | |
| Apr 7, 2021 at 20:44 | vote | accept | David Corwin | ||
| Apr 7, 2021 at 20:14 | history | edited | Dan Petersen | CC BY-SA 4.0 |
added 352 characters in body
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| Apr 7, 2021 at 19:40 | history | answered | Dan Petersen | CC BY-SA 4.0 |