Timeline for Terminology: lax vs. oplax colimits
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 4, 2010 at 17:37 | vote | accept | Reid Barton | ||
| Mar 3, 2010 at 6:04 | comment | added | Mike Shulman | If "in a 2-category 'op' refers to reversing the 1-cells" but "reversing the 1-morphisms in a 1-category is called 'co'," then wouldn't it follow that while we have limits and colimits in a 1-category, we would have limits and oplimits in a 2-category? But no one says that. It's true that in a 2-category, we write C^op to mean reversing the 1-cells and C^co for reversing the 2-cells, but in a 1-category we also write C^op for reversing the 1-cells, and nevertheless we use "co-" for most dualizations there. | |
| Mar 3, 2010 at 6:00 | answer | added | Mike Shulman | timeline score: 9 | |
| Mar 3, 2010 at 3:36 | comment | added | Tom Leinster | No, because reversing the (1-)morphisms in a (1-)category is called "co". So colimits are still colimits. Anyway, it's not that I'm a huge fan of the "op"/"co" system. It's that I don't understand why people choose to use the less common prefix ("op") when the more common one ("co") is logically correct. So, I merrily say "colax". | |
| Mar 3, 2010 at 2:26 | comment | added | Reid Barton | I agree in principle, but carrying this logic to its conclusion, don't we find that "colimits" in a 1-category should be called "oplimits"? Alternatively, reverse the notation C^op and C^co throughout. I don't see either of these happening... | |
| Mar 3, 2010 at 0:54 | comment | added | Tom Leinster | This is probably making things worse, but personally I've never understood why (some) people say "oplax" rather than "colax". In a 2-category, "op" refers to reversing the 1-cells and "co" refers to reversing the 2-cells. Here, we're reversing a 2-cell. Hence, it should be "co". Moreover, in the 1-categorical world, the standard prefix for dualization is "co", not "op". | |
| Mar 2, 2010 at 23:46 | answer | added | Finn Lawler | timeline score: 3 | |
| Mar 2, 2010 at 22:12 | history | asked | Reid Barton | CC BY-SA 2.5 |