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Started adjoint lifting theorem. For now, it only includes a version for lifting left adjoints (I still haven’t read Johnstone’s 1975 paper for the case of right adjoints). I hope there is no substantial error in the appliaction for cocompleteness.
Welcome the entry and welcome the contributor!
By the way, the only place where I know that people cite Categories for Working Mathematicians by “Categories Work” is nlab. When I saw it first time I was very confused. I find usage of non-insightful slang unfriendly to the outsiders (I count as an outsider in category theory). It makes categories not work for outsiders.
Thank you, Zoran!
Regarding “Categories Work,” I think that Mac Lane himself used it (in his Mathematics, Form and Function).
I hadn’t heard it before coming to the ’lab either, although I knew immediately what it meant when I heard it.
Added a sketch of proof in adjoint lifting theorem.
Looking over adjoint lifting theorem (a very useful result), it seems to me the proof could probably be made to look simpler by using string diagrams. I would undertake this myself, except that I am really no good at graphics. Perhaps I should hand-draw and upload, or do people have a better suggestion?
If you have another proof than it should be added to the existing, not replacing it. For example, I always had difficulty in understanding any categorical mathematics involving string diagrams so I am not a good audience for a string diagram involving proofs even if they are internally simpler.
I understand; you’re not alone. Yes, I was hoping just to add, not erase and replace.
By the same token, hand-drawn pictures would be better than no pictures!
I second Mike’s comment
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