Talk:Adjoint functors
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I'd have to agree with the comment that this page, for all its content, lacks motivation. Put it another way, such feeling as I have for the adjunction concept didn't come from reading this sort of account. It is more difficult to know exactly what to do about it. The sort of example that might help is the way implication in logic can be defined (introduced) as an adjoint. (But it depends on your background.)
Charles Matthews 17:51, 4 Nov 2003 (UTC)
Hmmm - generalised inverses - I'd have to say my understanding of the concept improved when I stopped trying to use this as an intuition.
Charles Matthews 12:08, 20 Feb 2004 (UTC)
Why the plural in the title? I realize that two functions are adjoints to each other, but the term can also be used in the singular: This functor is the adjoint of that functor. Michael Hardy 23:26, 22 Jul 2004 (UTC)
- FWIW, I came here typing "adjoint functors" in the search box. For singular, I would have typed "left adjoint" or "right adjoint f." BACbKA 20:50, 7 Aug 2004 (UTC)
- I agree that the title should be singular 145.97.223.187 17:32, 9 Mar 2005 (UTC)
Plural is better, really. Pair of adjoint functors is a fuller version. Left adjoint or right adjoint is OK; but 'adjoint functor' on its own is a bit like 'scissor', IMO. Charles Matthews 15:51, 16 Mar 2005 (UTC) See also stilts. Charles Matthews
- It is a little bit different, in that adjoint functors have a built-in asymmetry that scissors or stilts don't have...but agreed that left adjoint and right adjoint should still just redirect here. Revolver 05:38, 14 May 2005 (UTC)
- Adamek, Herrlich, and Strecker give a definition of "adjoint functor" and "co-adjoint functor", but I think these are just names for "left adjoint" and "right adjoint" (or the other way around), curiously, they don't bother to mention the relation to the usual left/right adjoint terminology. Revolver 05:35, 14 May 2005 (UTC)
I'd like an explanation of the notation in Adjoint functors#Formal_definitions. I found the beginning of one on pages 29 and 34 of [1] (http://www.math.upatras.gr/~cdrossos/Docs/B-W-LectureNotes.pdf) (they call Mor(), Hom()), but haven't done the work yet to elaborate it to fit here. Perhaps there should be another page defining the Mor Functor? JeffreyYasskin 18:48, 3 Apr 2005 (UTC)
Not really. Mor for morphism is more correct, pedantically speaking, but I suppose Hom for homomorphism is very common. Charles Matthews 20:26, 3 Apr 2005 (UTC)
- I changed from "Mor" to "hom" on the category pages just because that's the most widely used (e.g. Mac Lane, the standard reference). In an ideal world, "Mor" would have become the standard notation, but somehow that didn't happen. Both are common...once you're aware they mean the same thing, it shouldn't be confusing. Revolver 05:42, 14 May 2005 (UTC)