Timeline for Why forgetful functors usually have LEFT adjoint?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Oct 14, 2021 at 14:58 | comment | added | Rachid Atmai | When forgetful functors have left adjoints, those left adjoints will be the minimally required adjoints one can obtain: free constructions. The only properties that will hold are those who follow from the axioms of the free constructions (if my understanding is correct) | |
| Jan 8, 2015 at 17:21 | comment | added | Tim Campion | In fact, if the forgetful functor is $\mathsf{Set}$-valued, then it has a left adjoint if and only if it is representable. For base categories other than $\mathsf{Set}$, it's not quite so clear what it means to be representable. | |
| Oct 22, 2011 at 16:59 | comment | added | KotelKanim | Forgetful functors usually preserve limits because they are usually representable. | |
| Nov 22, 2009 at 21:08 | vote | accept | Yuhao Huang | ||
| Nov 21, 2009 at 17:13 | history | answered | SixWingedSeraph | CC BY-SA 2.5 |