Timeline for Making the conceptual leap from locales to Grothendieck topologies?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2015 at 0:24 | comment | added | Zhen Lin | The correct analogy is this: (Grothendieck sites) : (Grothendieck topos) :: (presentation of a frame) : (locale). | |
| Sep 27, 2015 at 22:41 | comment | added | user13113 | The other basic example of a Grothendieck topos is the category of $G$-sets for a group $G$, which I intuit as being a way that Grothendieck toposes can vary that is completely orthogonal to how locales vary. And those two options essentially cover all possibilities: every Grothendieck topos is (equivalent to) the category of sheaves for a localic groupoid. | |
| Sep 27, 2015 at 22:38 | comment | added | user13113 | The standard way to make a locale a site is that an object is covered by a collection of subobjects iff that object is the join of the (objects representing the) subobjects. Also, have you yet seen Lawvere-Tierney topology? | |
| Sep 27, 2015 at 22:10 | history | asked | Harrison Smith | CC BY-SA 3.0 |