Timeline for On the link between homology and homotopy
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2020 at 14:47 | comment | added | Fernando Muro | @Anonyme have a loot at Baues, Hans-Joachim. 2006. “Triangulated Track Categories.” Georgian Mathematical Journal 13 (4): 607–634. | |
| Aug 31, 2020 at 11:48 | comment | added | Amos Kaminski | @FernandoMuro Seem very interesting, could you please send reference ? thanks in advance. | |
| Aug 31, 2020 at 11:05 | comment | added | Fernando Muro | @anonyme not that much, just the homotopy 2-category. The homotopy category is constructed by taking sets of connected components on mapping spaces. For the homotopy 2-category you take fundamental groupoids instead. | |
| Aug 29, 2020 at 4:15 | comment | added | Amos Kaminski | @FernandoMuro Stable derivator ? Or something else | |
| S Aug 27, 2020 at 18:34 | history | bounty ended | Amos Kaminski | ||
| S Aug 27, 2020 at 18:34 | history | notice removed | Amos Kaminski | ||
| Aug 27, 2020 at 18:34 | vote | accept | Amos Kaminski | ||
| Aug 22, 2020 at 14:47 | answer | added | David White | timeline score: 1 | |
| Aug 22, 2020 at 14:24 | history | edited | David White | CC BY-SA 4.0 |
Fixed many grammar issues
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| Aug 21, 2020 at 17:54 | answer | added | Arthur Pander Maat | timeline score: 1 | |
| Aug 21, 2020 at 16:53 | comment | added | Fernando Muro | Just a remark: for functorial mapping cones, 2-categories suffice. | |
| S Aug 21, 2020 at 16:34 | history | bounty started | Amos Kaminski | ||
| S Aug 21, 2020 at 16:34 | history | notice added | Amos Kaminski | Draw attention | |
| Aug 18, 2020 at 19:32 | comment | added | Noah Riggenbach | probably Lunts and Orlovs paper has something about this. I'll check and get back to you | |
| Aug 18, 2020 at 16:15 | comment | added | Amos Kaminski | @NoahRiggenbach If you could give me a reference it's will help me a lot | |
| Aug 18, 2020 at 15:01 | comment | added | Noah Riggenbach | DG means differential graded. This means it's enriched over chain complexes. By the Dold-Kan correspondence this will give you an infinity category. As for why infinity categories help here, the idea is they make homotopy cofibers, and homotopy colomits in general, functorial. This is because they let you treat commuting up to homotopy as commuting, and let you treat rather complicated classes of weak equivalence like they were homotopy equivalences. | |
| Aug 18, 2020 at 13:47 | review | Close votes | |||
| Aug 21, 2020 at 16:36 | |||||
| Aug 18, 2020 at 13:39 | comment | added | Amos Kaminski | @NoahRiggenbach the fact that the derived category is not given by a universal property is equivalent in some sense to the fact that the cone is not functorial so i will be grateful if you could explain me how infinite category fix this ? and what do you mean by DG? thank you in advance | |
| Aug 18, 2020 at 13:26 | comment | added | Noah Riggenbach | As for why someone with a homological background might want to know about higher categories, there is this very annoying fact that the cone of a map is not a functorial construction. DG and infinity categories fix this | |
| Aug 18, 2020 at 11:55 | history | edited | Amos Kaminski | CC BY-SA 4.0 |
added 2 characters in body
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| Aug 18, 2020 at 11:30 | history | edited | Amos Kaminski | CC BY-SA 4.0 |
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| Aug 18, 2020 at 11:23 | history | asked | Amos Kaminski | CC BY-SA 4.0 |