Timeline for Two directed colimits of same spaces with different inclusions
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Jun 23, 2019 at 7:31 | comment | added | Andrea Marino | Yes! You are right. Both are fully faithful! | |
| Jun 23, 2019 at 1:42 | comment | added | Todd Trimble♦ | Thanks! The colimit in the second case is also known as a Prüfer group: en.wikipedia.org/wiki/Pr%C3%BCfer_group. The only thing I'd add to your proof is that the inclusion $Grp \to sSet$ is fully faithful, so that if the colimits on the simplicial set side were isomorphic, they'd have to be isomorphic on the group side, leading to a contradiction as you explained. | |
| Jun 23, 2019 at 0:52 | history | answered | Andrea Marino | CC BY-SA 4.0 |