Faithful functor

A faithful functor is a functor that is injective on hom-sets. If $𝐹 : 𝖢 \to 𝖣$ is a functor, then it is faithful 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 injective. #m/def/cat If it is also surjective, the functor is a Fully faithful functor.

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