Full functor

A full functor is a functor that is surjective on hom-sets. If $𝐹 : 𝖢 \to 𝖣$ is a functor, then it is full iff for any hom-set $𝖢 (𝑋, 𝑌)$ the associated mapping

𝐹 : 𝖢 (𝑋, 𝑌) \to 𝖣 (𝐹 𝑋, 𝐹 𝑌) 𝑓 \mapsto 𝐹 𝑓

is surjective. If it is also injective, the functor is a Fully faithful functor.

#state/tidy| #lang/en | #SemBr