Timeline for Topos with enough projectives
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2022 at 14:04 | history | edited | Morgan Rogers | CC BY-SA 4.0 |
fixed link
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| Jan 20, 2022 at 14:04 | comment | added | B. W. | The link to "this paper" is broken; what paper is talking about when a localic topos has enough projectives? | |
| Nov 9, 2019 at 10:00 | history | edited | Morgan Rogers | CC BY-SA 4.0 |
Answered detail previously added, should make question easier to answer.
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| Nov 9, 2019 at 8:45 | history | edited | Morgan Rogers | CC BY-SA 4.0 |
Added a detail to the question.
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| Dec 6, 2018 at 14:12 | comment | added | Tim Campion | Note also that there are subtleties lurking here -- for instance the distinction between a projective object and an internally projective object in a topos. | |
| Dec 3, 2018 at 23:03 | comment | added | Tim Campion | My guess (based on not much besides the presheaf example) would be that a topos has enough projectives if and only if its localic reflection has enough projectives. Maybe there's something to say about the hyperconnected-localic factorization system which would allow for such a reduction. | |
| Dec 1, 2018 at 21:49 | comment | added | Simon Henry | Note that the first class I mentioned (the topos that are only locally of the form in the paper) is considerably larger than the localic examples and contains lots of example that are not "determined by their sub-terminal objects". For example all presheaves categories over an indexing category that has only monomorphisms fits into this class. | |
| Dec 1, 2018 at 18:22 | comment | added | Morgan Rogers | Agreed: localic toposes provide good intuition generally, but since many toposes with enough projectives (especially presheaf toposes) are far from being determined by their subterminal objects, these are too restricted to be the whole story. | |
| Dec 1, 2018 at 17:49 | comment | added | Simon Henry | Hum, in second thought, there is also all presheaves toposes that have enough projective, and they are not all of the form I mentions above, so things are more complicated... | |
| Dec 1, 2018 at 17:35 | comment | added | Simon Henry | A larger class of topos that will satisfies this condition, is the toposes that are locally of the forms described in the paper. This corresponds exactly to toposes of equivariant sheaves over étale localic groupoid whose space of objects satisfies this condition of having a basis of dislocalbe objects. Similar results in topos theory suggest that this might be all of them, but I'm not quite sure yet. | |
| Nov 30, 2018 at 16:26 | history | asked | Morgan Rogers | CC BY-SA 4.0 |