Timeline for A categorical characterization of the lexicographic order
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2011 at 14:51 | answer | added | Buschi Sergio | timeline score: 3 | |
| Dec 8, 2011 at 22:51 | comment | added | David Roberts♦ | @Buschi - you are allowed to add an answer to your own question. You get more space and can format things better that way ;) | |
| Dec 8, 2011 at 22:50 | comment | added | David Roberts♦ | @Manny - it may be a non-symmetric monoidal structure on $Pos$, but this would preclude there being a definition via a universal property. Alternatively, since $Pos$ is a 2-category, it might be some sort of a lax 2-limit. In that case, the order is important, unlike limits in a 1-category. | |
| Dec 8, 2011 at 20:12 | comment | added | Buschi Sergio | I seems resolved it, need preorders: the lexicographic preorder $x\times_l y$ is the universal object for the preorders $a$ by two morphism $f: a\to x,\ g: a\to |y|$ (where $|y|$ is the underling set of $y$ (caotic preorder)) plus a third morphism $h: a'\to y$ (where $a'$=*"pullback of $f$ by $\Delta_x\to x$"*) such that $\eta\circ h=g\circ \alpha$ where $\alpha: a'\to a,\ \eta: y\to |y|$ naturals | |
| Dec 8, 2011 at 19:04 | comment | added | Buschi Sergio | Manny Reyes: sure, but isnt essential, anyway consider the "first" (the primary for the lexicographic order) as the one on the left. | |
| Dec 8, 2011 at 17:09 | comment | added | Manny Reyes | Notice that the lexicographic order depends on which poset you choose to list first. Thus if it is to satisfy a universal property, this property must also depend on the order of the two posets. | |
| Dec 8, 2011 at 16:54 | history | edited | Tom Leinster | CC BY-SA 3.0 |
fixed spelling and grammar; edited title
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| Dec 8, 2011 at 16:30 | comment | added | David White | I believe it's normally spelled "lexicographic" | |
| Dec 8, 2011 at 14:21 | history | asked | Buschi Sergio | CC BY-SA 3.0 |