Timeline for What does an endomorphism in a triangulated category give rise to?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22, 2014 at 0:15 | vote | accept | მამუკა ჯიბლაძე | ||
| Nov 21, 2014 at 23:48 | answer | added | Marc Hoyois | timeline score: 5 | |
| Nov 17, 2014 at 19:30 | comment | added | მამუკა ჯიბლაძე | @MarcHoyois Also, colimit/limit seemingly amount to universally turning $\varphi$ into an isomorphism (either "from the left" or "from the right"), but then one loses e. g. the case when $\varphi$ is nilpotent. Cannot one obtain something meaningful in this case too? | |
| Nov 17, 2014 at 19:27 | comment | added | მამუკა ჯიბლაძე | @MarcHoyois thank you for the explanation, and for the link. But could you please write (in an answer) how precisely one obtains a filtered object, and whether one needs just triangulated structure to get anything from it? In the link you provided seemingly one needs some enhancements. | |
| Nov 17, 2014 at 12:01 | comment | added | Marc Hoyois | No matter what the degree of $\phi$ is, it gives rise to a filtered object. If you apply a homological functor $H$ to it (e.g. map another object into it), you get two spectral sequences, potentially converging to $H$ of the limit and colimit of the filtered object: ncatlab.org/nlab/show/… | |
| Nov 17, 2014 at 11:29 | history | asked | მამუკა ჯიბლაძე | CC BY-SA 3.0 |