Timeline for Terminology: lax vs. oplax colimits
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 3, 2010 at 18:03 | comment | added | Finn Lawler | @Reid: I didn't really answer your question, did I? I think Mike's answer is better than mine, so I'd go along with him. In particular, I was probably wrong to suggest that (op)lax cones are defined simply by means of constant functors. For example, Johnstone, in the Elephant, uses the opposite convention for lax transformations, but he defines a lax cone as an oplax transformation out of a constant functor. He doesn't explain exactly why, but the ensuing Lemma 1.1.6 suggests that it's for the same reason that Mike gives. | |
| Mar 3, 2010 at 3:40 | comment | added | Tom Leinster | +1 Finn: that's a fantastically detailed n-Lab discussion that you linked to. I had no idea, in fact, that there was any controversy over the direction of lax transformations. Shows what I know. | |
| Mar 3, 2010 at 2:24 | comment | added | Reid Barton | Connecting the (op)lax convention for colimits to the convention for natural transformations makes a lot of sense. But do you have a sense of how the terms are used in the literature? Do people who have the opposite convention for lax natural transformation generally also have the opposite convention for lax limits and colimits? | |
| Mar 3, 2010 at 2:22 | comment | added | Reid Barton | Oops, I forgot that "lax colimit cone" means "cone which is actually a lax colimit". I just wanted to say "cone of the type appearing in the definition of lax colimit". | |
| Mar 2, 2010 at 23:46 | history | answered | Finn Lawler | CC BY-SA 2.5 |