Timeline for Why isn't pullback-stability defined for individual colimits but for colimits with the same shape?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 17, 2023 at 21:42 | history | became hot network question | |||
| Jul 17, 2023 at 17:13 | vote | accept | Linuxmetel | ||
| Jul 17, 2023 at 15:50 | comment | added | Peter LeFanu Lumsdaine | @NajibIdrissi: That’s a rather fallacious objection: many interesting properties of an object or diagram involve its relationships with other related objects and diagrams. As noted in my answer, OP’s definition is a very reasonable and fairly standard definition of pullback-stability of an individual colimit. | |
| Jul 17, 2023 at 15:46 | answer | added | Peter LeFanu Lumsdaine | timeline score: 12 | |
| Jul 17, 2023 at 15:38 | comment | added | Najib Idrissi | Well, $\mathrm{colim}_{d∈D}\ (G(d) \times_Z Y) \to (\mathrm{colim}_{d∈D}\ G(d))\times_Z Y$ is a different colimit than $\mathrm{colim}_D\ G$. So what you have defined is not a property of $\mathrm{colim}_D\ G$ because it depends on something else, namely, the functor $G(-) \times_Z Y$. | |
| Jul 17, 2023 at 14:12 | history | edited | Linuxmetel | CC BY-SA 4.0 |
added 331 characters in body
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| Jul 17, 2023 at 13:59 | comment | added | Linuxmetel | Thank you for your comment. I thought it was obvious, but I should have written it. I'll write it. | |
| Jul 17, 2023 at 13:51 | comment | added | Zhen Lin | Why don't you show us how you think it should be done, then? | |
| S Jul 17, 2023 at 13:40 | review | First questions | |||
| Jul 17, 2023 at 13:44 | |||||
| S Jul 17, 2023 at 13:40 | history | asked | Linuxmetel | CC BY-SA 4.0 |