Right. I've fixed my comment to make that clearer.

I found this absolutely mind-blowing when I first learned it: in rough terms,

"implies" is adjoint to "and"!!!


And when combined with all the other adjoints, including those involving \\(\exists\\) and \\(\forall\\), we get the feeling that logic is all about adjunctions!



> It seems like the chain \\(\Delta \dashv \, \wedge \dashv\, \to\\) is a little bit fictitious. By which I mean, \\(\wedge\\) is simultaneously denoting two different species: a binary operator and a family of unary operators, the former of which might not have a right adjoint, and the latter of which might not have left adjoints.

True. That chain is a sloppy way of talking about something... but that thing is real and amazing.