Definition 0.1. Let 𝒜 and ℬ be two categories and let F : 𝒜→ℬ be a functor. F is said to be a fully faithful functor if it is an isomorphism on every set Hom(−,−) of morphisms, and that it is essentially surjective if for every object X ∈ℬ, there is some Y ∈𝒜 such that X and F(Y ) are isomorphic.