Timeline for Idempotent completeness
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 13, 2023 at 14:42 | comment | added | Marc Hoyois | $X\mapsto P(X)$ is a sheaf of categories, so $P(X)$ is the limit of $P(U)$ as $U$ ranges over all affine opens of $X$. On the other hand, since idempotents and their images are preserved by arbitrary functors, a limit of idempotent complete categories is again idempotent complete. Thus $P(X)$ is idempotent complete. | |
| Sep 12, 2023 at 10:04 | comment | added | user443060 | If you could please elaborate a little it would mean a lot to me. | |
| Sep 12, 2023 at 7:49 | comment | added | Marc Hoyois | $P(X)$ is a limit of categories of the form $P(R)$, and limits preserve idempotent completeness. | |
| Sep 12, 2023 at 5:05 | history | asked | user443060 | CC BY-SA 4.0 |