Timeline for Grothendieck toposes in (very) weak foundation
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jul 3, 2017 at 15:09 | history | suggested | Matthieu FG |
added cat log tag
|
|
| Jul 3, 2017 at 14:52 | review | Suggested edits | |||
| S Jul 3, 2017 at 15:09 | |||||
| Aug 14, 2015 at 10:02 | comment | added | Simon Henry | Indeed we can, but as I mentioned it is not clear that sheaves should be a subcategory of small presheaves (the situation might be similar to what happen when you have a large site: the sheafification of a small presheaves might not be a small presheaf and what we want to consider is the category sheaves which are sheafication of small presheaves), in which case the closure operation is not a solution either... | |
| Aug 14, 2015 at 9:35 | comment | added | Zhen Lin | We can think about universal closure operators instead of local operators. | |
| Aug 14, 2015 at 9:20 | answer | added | Todd Trimble | timeline score: 5 | |
| Aug 14, 2015 at 7:59 | comment | added | Simon Henry | That is indeed interesting. But Under weak fundation Grothendieck toposes are not going to be elementary topos, they are not expected to be cartesian closed if "sets" is not, and they are not going to have power objects if there is no power objects in "sets", so I'm sure one can use locale operators here either. | |
| Aug 14, 2015 at 0:20 | comment | added | David Roberts♦ | Simon, you may be interested to know that there are (non-Grothendieck) boolean toposes that are not locally small: as such they have internal homs, which are the 'correct' 'set' of functions (working in the internal logic). These correspond to certain class-forcing models. Regarding a Grothendieck topology, one could replace it by a Lawvere-Tierney topology/local operator and see what one gets. | |
| Aug 13, 2015 at 20:42 | comment | added | Todd Trimble | The section "Weak Foundations" first appears in Revision number 27, written by Toby Bartels. I may drop him a note about your post. | |
| Aug 13, 2015 at 20:34 | history | asked | Simon Henry | CC BY-SA 3.0 |