\begin{definition}[Definition:Left Adjoint Functor]
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 $G$ {{iff}} there exists an adjunction $\struct {F, G, \alpha}$.
\end{definition}