Types of functors

Faithful functor

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

𝐹:𝖢(𝑋,𝑌)→𝖣(𝐹𝑋,𝐹𝑌)𝑓↦𝐹𝑓

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

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