Definition:Full Functor

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Definition

Let $\mathbf C$ and $\mathbf D$ be metacategories.

Let $F: \mathbf C \to \mathbf D$ be a covariant functor.


Then $F$ is full if and only if for all objects $C_1, C_2$ of $\mathbf C$:

$F: \map {\operatorname{Hom}_{\mathbf C} } {C_1, C_2} \to \map {\operatorname{Hom}_{\mathbf D} } {F C_1, F C_2}, \ f \mapsto F f$

is a surjection.

Here $\operatorname{Hom}$ signifies a hom class.


Also see


Sources