Definition:Left Adjoint Functor

Definition
Let $\mathbf C$, $\mathbf D$ be locally small categories.

Let $F : \mathbf D \to \mathbf C$ and $G : \mathbf C \to \mathbf D$ be functors.

$F$ is a left adjoint functor of $G$, if there exists an adjunction $(F,G,\alpha)$.