Timeline for Small categories and completeness
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 4, 2012 at 10:37 | comment | added | Shlomi A | @Fernando, thanks. It seems that a poset with $\kappa $ objects and a maximal element works if one requires all colimits of cardinality $\leq \kappa$. However, I haven't managed to convince myself that such a category (2) must be a poset. | |
| Oct 4, 2012 at 6:00 | comment | added | Fernando Muro | @Shlomi, probably not, now I'd go to prove that any category with your conditions in (2) is a poset, have a try. | |
| Oct 3, 2012 at 22:14 | comment | added | Shlomi A | Colimits is fine for me. Your example of vector spaces of dimension $< \kappa $ is clear. However, is there some more general argument that shows that any small category with $Ob(\mathcal C)$ of cardinality $\kappa $ *cannot* have all colimits of size $\kappa$? | |
| Oct 3, 2012 at 19:32 | history | answered | Fernando Muro | CC BY-SA 3.0 |