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A comparatively long and technical section “From hom-functors to units and counits” (on adjoint functors) was sitting inside the Idea-section of adjunction. It seemed plainly misplaced there, and distracting attention from what should be the content of this entry, as opposed to the entry adjoint functor. So I have moved it now to where it seems to belong: inside the Examples-section.
The diagrams in Direct Definition do not seem to be rendering properly. (Not really my observation; I was alerted in a chat room at MO).
Probably need to be re-done with tikz.
Thanks. I have added the publication data, too.
Hmm, but maybe these should be in adjoint functor. We’re running this page adjunction as an abstract 2-categorical concept, although ’adjoint functors’ makes up a large chunk of the page as an example.
Yeah, I have already done some harmonizing of the list of References to both entries. That’s just the way it is now. At least each References section is now alerting the reader to also look at the other.
We should rewrite them in Tikz or xymatrix. I believe Urs already did so in one form at triangle identities, and I recall having done so myself in a different form somewhere, though I do not remember where just now; we can just copy the code over. (Edit: the ones I wrote are at left adjoint. I will fix this myself tomorrow if no-one gets to it before me.)
The ’Examples’ section on this page is rather a mess. Apart from the fact that the contents are mostly not really examples, it would be good if some industrious reader can re-work the material into some structure (proposition, proof, remark, example etc).
Following Richard in #12 I have tried to bring the old material under “Examples – Adjoint functors” (here) into some shape: I have added Proposition/Example/Proof/Remark-environments and slightly adjusted the text here and there. (One could still improve the “Proof” to make the converse implication more explicit.)
Also added pointer to the proof of this that I once wrote at adjoint functor here.
This paragraph should probably rather go the page adjoint functor. I have copied it to there.
Ah, I thought the page adjunction was looking barer than I remembered; I didn’t recall that there were two pages.
Right, it can be confusing. So I have added a disambiguation line to the very top of the entry, prominently pointing to the page adjoint functors.
Also moved the paragraph on slice categories to there.
also tried to streamline the Idea-section (here)
The entry is still lacking an “original reference” for the notion of adjunction in general 2-categories, if such exists. Just in order to have at least one reference earlier that Johnson & Yau (2020), I have now added pointer to:
Thanks!
I have added more details, such as a link to the article:
added pointer to:
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