full functorFullFunctor2004-05-11 02:12:572004-05-11 02:12:57Definition% this is the default PlanetMath preamble. as your knowledge
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A functor $T:\mathcal{C}\to\mathcal{D}$ is \emph{full} if the \emph{arrow function} of $T$ is surjective for every
pair of objects in $\mathcal{C}$. More precisely, for every pair $C_1, C_2\in \operatorname{Ob}(\mathcal{C})$, the
arrow function $T_{(C_1,C_2)}$ of $T:$
$$T_{(C_1,C_2)}:\operatorname{hom_{\mathcal{C}}}(C_1,C_2)\to\operatorname{hom_{\mathcal{D}}}(T(C_1),T(C_2))$$
given by $T_{(C_1,C_2)}(f)=T(f)$ is a surjection.