Timeline for Initial cones, terminal cocones
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2023 at 18:10 | comment | added | Emily | I think the special case of suprema illustrates this nicely: you can express these as colimits in posets, and they are interesting because they are the "smallest element larger than every element in the indexing set", but a terminal cocone would be the "smallest element smaller than every element in the indexing set", so the notion ends up reducing to just the minimal element of the poset and thus is not so interesting in general. (This is just a special case of Simon's comment, of course) | |
| Apr 4, 2023 at 17:41 | comment | added | Simon Henry | If the category has an initial object or a terminal object then the initial cone or terminal cocone are just these. So in most categories where one might want to consider this type of notion, it collapses to a simpler one. | |
| Apr 4, 2023 at 17:36 | history | asked | Alec Rhea | CC BY-SA 4.0 |