Timeline for Homotopy equivalences and Mapping Cones
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 11, 2020 at 14:32 | vote | accept | physician | ||
| Aug 11, 2020 at 14:32 | comment | added | physician | Thank you very much, it's very clear now. Indeed part of the question was meant to ask "how to think of this property conceptually". Triangulated categories seems to be the answer as you very nicely explain. (I doubt I would've gotten that suggestion on SE :) ) | |
| Aug 10, 2020 at 23:04 | comment | added | Marco Farinati | I have expanded my answer, I hope it helps. Just as final comment, this is more an ME question than an MO one :) | |
| Aug 10, 2020 at 23:00 | history | edited | Marco Farinati | CC BY-SA 4.0 |
added 2373 characters in body
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| Aug 10, 2020 at 21:20 | comment | added | physician | Please check the edit to the original question where I've clarified some of the ambiguities. $g, h$ are specific maps. | |
| Aug 10, 2020 at 7:16 | comment | added | D.-C. Cisinski | Sure, the direction you suggest is the right one! | |
| Aug 10, 2020 at 1:43 | comment | added | Marco Farinati | Please take my answer as a sugestion into that directioin | |
| Aug 10, 2020 at 1:41 | comment | added | Marco Farinati | Well, I didn 't check everything.. may be my answer lack of some coherence. In any case, Í think the question should definitely be directioned to the language of the homotopy category as a triangulated one. Plade take my answer a | |
| Aug 9, 2020 at 23:58 | comment | added | D.-C. Cisinski | I disagree: it would look like a reasonable statement if 1. meant "there exists $f:A\to B$ such that the cone of $f$ is chain homotopic to $C$". But, since $f$ is given a priori, and since there are no relations between $f$ and the data appearing in conditions 2. or 3., there is no way we may prove that these statements are equivalent. Condition 2. or 3. could be true with $f=0$, for instance. | |
| Aug 9, 2020 at 19:41 | history | answered | Marco Farinati | CC BY-SA 4.0 |