Timeline for Which direction of the adjoint functor theorem is most useful?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 14, 2021 at 19:05 | comment | added | Robert Furber | @AndrejBauer My mnemonic for (a) is "Left adjoints should preserve Limits because they both have an L, but that would be too easy so it must actually be Colimits". | |
| Feb 14, 2021 at 16:52 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading
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| Feb 13, 2021 at 20:20 | answer | added | Tim Campion | timeline score: 10 | |
| Jan 27, 2021 at 17:50 | comment | added | Paul Taylor | If you can show that a functor preserves limits in some simple cases, that is empirical evidence suggesting that you try to find the right adjoint. The existence of the adjoint in general is far from trivial and may depend on the Axiom-Scheme of Replacement. I can't imagine that anyone would rely on that route as the public proof of existence. Besides, a construction is always better, even if you're classical. | |
| Jan 25, 2021 at 19:06 | review | Suggested edits | |||
| Jan 25, 2021 at 20:02 | |||||
| Jan 25, 2021 at 4:53 | comment | added | David Roberts♦ | I was going to add the link ncatlab.org/nlab/show/adjoint+functor+theorem to the original question, but then it would be odd, since it really only applies to b), as others have pointed out. | |
| Jan 25, 2021 at 2:36 | comment | added | Todd Trimble | Usually when someone asks on MO whether a functor has an adjoint and the answer is not obvious, I reflexively go for the contrapositive of (a). | |
| Jan 25, 2021 at 2:00 | comment | added | Mike Shulman | Regarding the actual question, my guess would be that (a) is used more often than (b). But I'm not sure how anyone could give a definitive answer. | |
| Jan 24, 2021 at 23:24 | comment | added | Andrej Bauer | Steve Awodey taught me (a) as the mnemonic "RAPL", probably because it sounds better than "LAPC". | |
| Jan 24, 2021 at 23:13 | comment | added | Dick Johnson | @Mike: Good to know, thanks! | |
| Jan 24, 2021 at 22:56 | comment | added | Mike Shulman | FWIW, in my experience usually when people say "the adjoint functor theorem" they are referring only to (b). Property (a) isn't generally given a special name. | |
| Jan 24, 2021 at 22:45 | history | asked | Dick Johnson | CC BY-SA 4.0 |