Let $\oppairi{\mathscr{A}}{\mathscr{B}}{F}{G}$ be categories and functors. We say that $F$ is left adjoint to $G$, and $G$ is right adjoint to $F$, and write $F \dashv G$, if \(\mathscr{B}(F(A), B) \cong \mathscr{A}(A, G(B))\) naturally in $A \in \mathscr{A}$ and $B \in \mathscr{B}$. The meaning of `naturally’ is defined below. An adjunction between $F$ and $G$ is a choice of natural isomorphism~.