Timeline for What to call a morphism of sites inducing an equivalence on categories of sheaves?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2021 at 20:04 | vote | accept | John Pardon | ||
| Oct 28, 2019 at 15:20 | comment | added | Simon Henry | The correct reference for the most general version of the comparison lemma is Moerdjik & Kock "Presentation of etendues" numdam.org/article/CTGDC_1991__32_2_145_0.pdf see the end of section 2. It is not claimed in the paper, but if I remember correctly the conditions they give are necessary and sufficient. | |
| Oct 28, 2019 at 14:45 | answer | added | Tim Campion | timeline score: 2 | |
| Oct 28, 2019 at 8:10 | comment | added | user147129 | The comparison lemma of SGA 4 (Expose 3, 4.1) is specifically about fully faithful functors, so that would be a very inaccurate reference in the generality of the question. Morita equivalence is indeed the term used in topos theoretic references (e.g. Caramello uses that term a lot). I don’t think I’ve seen it come up in algebraic geometry literature before. | |
| Oct 28, 2019 at 3:41 | comment | added | David Roberts♦ | Sometimes people describe it as 'satisfying the comparison theorem' or words to that effect, citing something in SGA4. The precise hypotheses or definitions that go into that theorem may not be what you have in mind, but I think it's a reasonable claim. | |
| Oct 28, 2019 at 2:02 | history | asked | John Pardon | CC BY-SA 4.0 |