Given two categories and functors between them:
We say that $F$ is left adjoint to $G$, and $G$ is right adjoint to $F$, and write $F ⊣ G$, if
$$ Hom_{\mathscr{B}}(F(A), B) ≅ Hom_\mathscr{A}(A, G(B)) $$
Given two categories and functors between them:
We say that $F$ is left adjoint to $G$, and $G$ is right adjoint to $F$, and write $F ⊣ G$, if
$$ Hom_{\mathscr{B}}(F(A), B) ≅ Hom_\mathscr{A}(A, G(B)) $$