Timeline for Grothendieck Topologies versus Pretopologies
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 6, 2012 at 2:25 | history | edited | David Roberts♦ | CC BY-SA 3.0 |
added 44 characters in body
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| Aug 3, 2012 at 18:04 | comment | added | Mike Shulman | More generally, a topology -- as opposed to a pretopology -- is uniquely determined by its category of sheaves (as a subcategory of the category of presheaves). | |
| Aug 3, 2012 at 10:05 | comment | added | David Roberts♦ | Hmm, you're right. I'll take out the first one. | |
| Aug 3, 2012 at 5:25 | comment | added | Mike Shulman | Nope. A sheaf on the open cover site must be trivial over the empty manifold; the other ones don't even force that. | |
| Aug 3, 2012 at 0:36 | comment | added | David Roberts♦ | Hmm, I guess you are right. But don't they all give the same category of sheaves? There might be a span of sites connecting the first of the above to each of the others. | |
| Aug 2, 2012 at 22:52 | comment | added | Mike Shulman | I think the first one is only equivalent to the other three if you add the extensive topology to those. | |
| Jul 30, 2012 at 7:54 | history | answered | David Roberts♦ | CC BY-SA 3.0 |