Types of functors

Fully faithful functor

A fully faithful functor is a functor that is bijective on hom-sets. cat If 𝐹 :𝖢 →𝖣 is a functor, then it is fully faithful iff for any hom-set 𝖢(𝑋,𝑌) the associated mapping

𝐹:𝖢(𝑋,𝑌)→𝖣(𝐹𝑋,𝐹𝑌)𝑓↦𝐹𝑓

is bijective. That is to say every morphism 𝐹𝑋 →𝐹𝑌 is the image of exactly one morphism 𝑋 →𝑌. Fully faithful functors preserve relationships between objects in a category.

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