Timeline for What is the most useful non-existing object of your field?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 15, 2019 at 17:18 | comment | added | Pietro Majer | (Yes, the third non-existent object was expressly ungiven :) ) | |
| Sep 29, 2014 at 12:38 | comment | added | Todd Trimble | Maybe it should be added that free suplattices on any set exist, and suplattices admit arbitrary infs (so are complete). Here, the morphisms of $\mathbf{SupLat}$ preserve just sups. Similarly, the free inf-lattice exists on any set, and this admits arbitrary sups. It's when we require morphisms of the category to preserve both arbitrary sups and infs that free objects do not exist (on sets of cardinaility greater than 2). | |
| Sep 29, 2014 at 12:11 | comment | added | Pietro Majer | Sorry, I should have called it "lattice" (fixed). Much less relations, thus a much wider generated class. | |
| Sep 29, 2014 at 12:05 | history | edited | Pietro Majer | CC BY-SA 3.0 |
correct
|
| Sep 29, 2014 at 11:14 | comment | added | Eric Wofsey | @AndréHenriques: Actually, it has $2^8$ elements. But you are correct that free complete Boolean algebras on finite sets exist (and are the same as free Boolean algebras). Free complete Boolean algebras on infinite sets do not exist. | |
| Sep 29, 2014 at 10:21 | comment | added | André Henriques | So, naively, I would guess that the free Boolean algebra on 3 generators has 8 elements, and is thus complete. Am I wrong? | |
| Sep 29, 2014 at 9:19 | comment | added | Toby Bartels | The third example does not exist, which is exactly what we're looking for! | |
| Sep 29, 2014 at 8:05 | comment | added | jmc | I really like your way of counting (-; | |
| S Sep 29, 2014 at 7:47 | history | answered | Pietro Majer | CC BY-SA 3.0 | |
| S Sep 29, 2014 at 7:47 | history | made wiki | Post Made Community Wiki by Pietro Majer |