Timeline for On the limit of a directed system of sheaves
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 27, 2018 at 13:59 | comment | added | BrianT | I understand. Then I want to assume that $X$ is the direct limit as topological space. | |
| Aug 27, 2018 at 13:57 | comment | added | Tom Goodwillie | That is, the direct limit in the category of topological spaces. So that a set in $X$ is open (or closed) iff for each $i$ its intersection with $X_i$ is open (or closed) in $X_i$. | |
| Aug 27, 2018 at 13:02 | comment | added | BrianT | Don't the inclusions $X_i \subset X_j$, $i \leq j$ imply that the direct limit is the union ? If not, then sorry for my lack of precision. I assume that the space $X$ is the direct limit of $X_i$. | |
| Aug 27, 2018 at 12:58 | comment | added | Tom Goodwillie | When you say "exhausting", do you simply mean that the $X$ is the union of the point sets $X_i$, or are you assuming that as a topological space $X$ is the direct limit of $X_i$? | |
| Aug 27, 2018 at 12:49 | comment | added | BrianT | $\mathcal{F}_i$ is a sheaf on $X_i$, that's the problem | |
| Aug 27, 2018 at 12:34 | comment | added | Tom Goodwillie | Is $\mathcal F_i$ a sheaf on $X$ or a sheaf on $X_i$? | |
| Aug 27, 2018 at 12:09 | history | asked | BrianT | CC BY-SA 4.0 |