Fully faithful functor

A fully faithful functor is a functor that is bijective on hom-sets. #m/def/cat If $𝐹 : 𝖢 \to 𝖣$ is a functor, then it is fully 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 bijective. That is to say every morphism $𝐹 𝑋 \to 𝐹 𝑌$ is the image of exactly one morphism $𝑋 \to 𝑌$ . Fully faithful functors preserve relationships between objects in a category.

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