Timeline for Complete the following sequence: point, triangle, octahedron, . . . in a dg-category
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2017 at 2:32 | vote | accept | John Pardon | ||
| Apr 19, 2016 at 8:39 | answer | added | Piotr Achinger | timeline score: 11 | |
| Apr 19, 2016 at 7:33 | answer | added | მამუკა ჯიბლაძე | timeline score: 10 | |
| Apr 18, 2016 at 19:30 | comment | added | Dylan Wilson | The diagram is produced algorithmically. If you want to do it for n composable morphisms, draw a them in a line. Now extend the line to the right with a zero, and down on the left with a zero. Now fill in this rectangle with pushout diagrams (so you're looking at an [n+1] \times [1] diagram.) Now on the far lower right you can extend by a map to 0, and on the lower left offset by one you can extend by zero... rinse wash and repeat. You get a staircase lookin' thing. | |
| Apr 18, 2016 at 19:26 | comment | added | მამუკა ჯიბლაძე | @DylanWilson Are you sure it is on p.24? I see there (TR4) and it is certainly not evident for me how to generalize this. | |
| Apr 18, 2016 at 18:57 | comment | added | Dylan Wilson | (It is not known whether any triangulated thing is n-angulated, but any stable $\infty$-category is $n$-angulated for any $n$, and the proof is the same as in loc. cit.) | |
| Apr 18, 2016 at 18:55 | comment | added | Dylan Wilson | the picture at the bottom of p.24 here: math.harvard.edu/~lurie/papers/HA.pdf has an evident generalization to any n-tuple of morphisms. If you write it down you'll join the group of m people who have independently discovered the notion of an "n-angulated category". The shape you seek comes from collapsing that unrolled version in some probably not-so-trivial way. | |
| Apr 18, 2016 at 17:30 | history | edited | John Pardon | CC BY-SA 3.0 |
added 45 characters in body
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| Apr 17, 2016 at 21:33 | history | asked | John Pardon | CC BY-SA 3.0 |