Timeline for Non-trivial automorphisms and descent
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| May 3, 2022 at 12:47 | comment | added | user481494 | @ZhenLin Thanks! Yes, that totally makes sense. I just thought there's more behind the quote, or other ways of making it precise. (I have never heard someone talking about automorphisms of points, rather than of spaces or algebraic structures, so I thought maybe there's some subfield in which one defines something like that on which your quote is based.) | |
| May 2, 2022 at 8:43 | history | became hot network question | |||
| May 2, 2022 at 8:43 | answer | added | Peter LeFanu Lumsdaine | timeline score: 6 | |
| May 2, 2022 at 5:55 | comment | added | Alec Rhea | An effective descent morphism $f$ in a category is an arrow such that the 'pullback along $f$' functor exists and is monadic, to address 3. | |
| May 2, 2022 at 1:26 | answer | added | Dmitri Pavlov | timeline score: 5 | |
| May 1, 2022 at 23:08 | comment | added | Zhen Lin | If I say that a groupoid is a kind of generalised set where the points may have non-trivial automorphisms, does that make sense? Every Grothendieck topos is equivalent to the category of sheaves on some localic groupoid, and localic groupoids are to locales as ordinary groupoids are to sets. | |
| May 1, 2022 at 20:22 | comment | added | Reid Barton | This looks like more than one question. | |
| May 1, 2022 at 19:37 | comment | added | მამუკა ჯიბლაძე | Re Question 2: view $f:\mathcal F\to\mathcal E$ as some sort of "resolution" of a complicated space impersonated by $\mathcal E$ by means of a simpler space impersonated by $\mathcal F$. A representative example is when $\mathcal F$ corresponds to the space of objects of a localic groupoid, $\mathcal E$ is the topos of equivariant sheaves, and to reconstruct $\mathcal E$ from $\mathcal F$ one also needs to know the "gluing data" in form of the space of morphisms of the groupoid. | |
| May 1, 2022 at 19:31 | comment | added | მამუკა ჯიბლაძე | Re Question 1: a localic groupoid has the space of objects ("points") and the space of morphisms. The groupoid structure in particular equips each point $p$ with a (localic) "group of automorphisms" - consisting of morphisms from $p$ to $p$. | |
| S May 1, 2022 at 19:06 | review | First questions | |||
| May 1, 2022 at 19:25 | |||||
| S May 1, 2022 at 19:06 | history | asked | user481494 | CC BY-SA 4.0 |