\[ F \dashv U \]

\[ ({-} \otimes A) \dashv \Hom(A, {-}) \]

Dualities play an important role in mathematics and they can be described with the help of equivalences between categories. In other words, many important mathematical theorems can be translated as statements about the existence of adjoint functors, sometimes satisfying additional properties. This is sometimes taken as expressing the conceptual content of the theorem.
Marquis, J.P., “Category Theory”, The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.) (Link)