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Between a lack of sleep, checking the nLab, and thinking about breakfast, I have come to realise that right adjoints are acidic (like orange juice) and left adjoints are alkaline (like coffee). Of course, this means that you have to identify the original functor (whatever you’re taking the adjoint of) with milk.
More seriously, right and left adjoints have a very definite difference in feeling, and I may just be hallucinating that this matches the difference between sour and bitter tastes (which I never noticed before), but surely other people have also felt a difference. I wonder if there is any consistency here?
But whilst coffee tastes okay with milk, orange juice tastes just awful. So are left adjoints better?
When I am on the edge of sickeness in fact, often the quickest recovery is taken milk and orange juice one after another, in lareg quantity and sleep after that. Calcium and C-vitamin get better absorbed together, I think. As far as intuition, I would rather think of left adjoints like base extension being acidic, sharp, opposite to what Toby feels.
Talk me through these feelings with the underlying functor from Top to Set as left adjoint to CoDisc and right adjoint to Disc.
Cow’s milk is actually slightly acidic. Wouldn’t water be a better liquid for the original functor? And how would you taste an ambijunction?
Weird discussion! I don’t think I ever have actual taste sensations associated with such concepts. I do sometimes experience math in a tactile way, but I don’t think I could easily put that into words.
When I am on the edge of sickeness in fact, often the quickest recovery is taken milk and orange juice one after another
So Zoran, you cure sickness with a monad?
Zoran’s remark reminds me of the old joke:
Patient to Doctor: You said last week that I should have an orange juice after a hot bath. I could just about manage the bath but I was then too full to drink the orange juice.
They say the old jokes are best but I beg to disagree.;-(
Oh, I got a chuckle over it! As well as over Tom’s question.
So Zoran, you cure sickness with a monad?
Regarding the repetitions, if not with a monad, one finds a cure in some term of the associated standard complex.
Cow’s milk is actually slightly acidic. Wouldn’t water be a better liquid for the original functor?
I thought of that afterwards. But I was thinking of breakfast drinks. Not that one can’t drink water at breakfast! (And I drank none of these, nor even the tea that I was actually planning to drink.)
I was also thinking of using milk as a buffer, something to add to coffee to take away the bitter edge. Obviously water would work almost as well, but American coffee is weak enough as it is! (Joke for the Europeans, you’re welcome.) Milk is also effective against chili peppers, which for some reason also feel like right adjoints to me, although in fact capsaicin is alkaline, and milk binds to it with a protein (completely different chemistry).
FWIW, taste is not the primary feeling here for me. I was just thinking about breakfast when I wrote the OP.
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