Timeline for Product in undercategory
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2011 at 12:17 | comment | added | Todd Trimble | Yes, I know. But sometimes a little light can be shed with a mild extra hypothesis. Knowing that co-slices are categories of algebras, and that slices are categories of coalgebras, can come in handy on occasion, even if you have to assume a little extra hypothesis. That's really the reason for giving my answer -- to share a factoid that could come in handy for someone one day. I hope you don't mind! | |
| Nov 28, 2011 at 8:24 | comment | added | Martin Brandenburg | A bit more serious: Your proof only works if $X$ has coproducts. But the fact that $A/X \to X$ creates and preserves limits holds in general. If $X$ has coproducts, I would just use that $A \coprod -$ is left adjoint to $A/X \to X$. | |
| Nov 27, 2011 at 22:05 | comment | added | Todd Trimble | Okay, I won't. :-) It's just another point of view, and may carry some resonance for some readers. If it doesn't, then fine. | |
| Nov 27, 2011 at 21:07 | comment | added | Martin Brandenburg | @Todd: Do you cite that M is closed under composition for (E,M)-structured categories when you want to explain someone that the composition of two injective maps is injective? ;) (Do not take this comment too seriously) | |
| Nov 27, 2011 at 18:40 | history | answered | Todd Trimble | CC BY-SA 3.0 |