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

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

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.