Timeline for Why forgetful functors usually have LEFT adjoint?
Current License: CC BY-SA 2.5
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Nov 23, 2009 at 9:22 | comment | added | alekzander | If you're just talking about the adjectives left/right, well .. that's terminology, sure, since you're talking about .. terms. There was some usage historically of "adjoint"/"coadjoint", but it's unnatural AFAIAC to say that one is in the "correct" (I guess I have to avoid the word "right" here) direction. However, we do have "unit"/"counit", so it wouldn't be a stretch to associate "adjoint" with "unit", and co-. I think this isn't done mostly because it was historically not used consistently this way (or that's what I gleaned from a comment in MacLane). | |
| Nov 23, 2009 at 3:05 | comment | added | Harrison Brown | Erm, I meant that, as far as I know, the reason we call left adjoints left and right adjoints right is basically entirely historical and has much more to do with arbitrary mathematical notation than any real difference between them. (I mean, yes, they're different, but not that different.) | |
| Nov 23, 2009 at 1:46 | comment | added | alekzander | In what way do you mean "mostly just terminology"? As Mark Hovey's topological example (an exercise in MacLane, also) points out, one may have both a left and a right adjoint which are clearly distinct. | |
| Nov 21, 2009 at 21:03 | history | answered | Harrison Brown | CC BY-SA 2.5 |