Timeline for Self-dual Complete Category
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 22, 2011 at 2:04 | comment | added | Harry Gindi | Commutative monoid =(. | |
| Jan 18, 2011 at 19:51 | comment | added | Buschi Sergio | Yes, right, sorry for my mistake | |
| Jan 17, 2011 at 20:34 | comment | added | Tom Leinster | arsmath is right: a monoid, regarded as a one-object category, is complete iff it is cocomplete iff it is trivial. Indeed, if it is complete then it has a terminal object, which must be the unique object; and this says that the monoid is trivial. | |
| Jan 17, 2011 at 20:29 | vote | accept | arsmath | ||
| Jan 17, 2011 at 18:48 | comment | added | arsmath | But is that category complete? I would think it's only complete when the monoid only has one element. | |
| Jan 17, 2011 at 16:43 | comment | added | Buschi Sergio | arsmath: You can see a monoid is a one-objet category $\mathscr{C}$. Then the the identity maps on objets and morphisms are a funtor isomorphism $\mathscr{C}\cong \mathscr{C}^{op}$ iff $\mathscr{C}$ as monoid is abelian. | |
| Jan 17, 2011 at 14:21 | answer | added | Todd Trimble | timeline score: 13 | |
| Jan 16, 2011 at 13:28 | comment | added | arsmath | I don't understand the abelian monoid example. | |
| Jan 16, 2011 at 13:28 | comment | added | arsmath | That's a great example, Denis-Charles. | |
| Jan 16, 2011 at 9:16 | comment | added | Buschi Sergio | Any abelian monoid. | |
| Jan 16, 2011 at 4:57 | answer | added | Mike Shulman | timeline score: 14 | |
| Jan 15, 2011 at 23:02 | comment | added | Martin Brandenburg | @Denis-Charles: Nice! | |
| Jan 15, 2011 at 23:00 | answer | added | Martin Brandenburg | timeline score: 1 | |
| Jan 15, 2011 at 22:54 | comment | added | D.-C. Cisinski | $C\times C^\mathit{op}$ for $C$ complete and cocomplete. | |
| Jan 15, 2011 at 21:35 | history | asked | arsmath | CC BY-SA 2.5 |