A $1$-morphism $f\colon A\to B$ of $\mathcal{C}$ is corepresentably full if, for each $X\in \text{Obj}\webleft (\mathcal{C}\webright )$, the functor

\[ f^{*}\colon \mathsf{Hom}_{\mathcal{C}}\webleft (B,X\webright )\to \mathsf{Hom}_{\mathcal{C}}\webleft (A,X\webright ) \]

given by precomposition by $f$ is full.


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