Definition:Left Adjoint Functor

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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 $(F,G,\alpha)$.