Timeline for Example of non-transitive homotopy relation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 17, 2023 at 8:09 | vote | accept | Igor Sikora | ||
| Mar 16, 2023 at 21:24 | history | became hot network question | |||
| Mar 16, 2023 at 16:38 | answer | added | Tyler Lawson | timeline score: 11 | |
| Mar 16, 2023 at 16:09 | comment | added | Simon Henry | ... and In the second case, the precise definition of cylinder you are using might be relevant as well. | |
| Mar 16, 2023 at 16:07 | comment | added | Simon Henry | When looking at non-cofibrant objects the left homotopy relation become ill-defined in the sense that it depends on the choice of the cylinder. Do you want an example of a single cylinder for $A$ such that the homotopy relation defined relative to this cylinder isn't transitive, or do you want an exemple in the case where le left homotopy relation is defined as "there exists a cylinder $IA$ and a map $IA \to X$? I think these are fairly different questions. (though I don't have an example for any - so maybe there is an answer that works for both). | |
| Mar 16, 2023 at 12:58 | comment | added | cheyne | I'm just asking for my own education... it seems you have to find some non-cell complex A in Top which is not cofibrant, then study the l.h.r. on Hom(A,X) and find your counter example there? | |
| Mar 16, 2023 at 12:43 | history | asked | Igor Sikora | CC BY-SA 4.0 |