PlanetPhysics/Fully Faithful Functor 2

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Let $𝒜$ and $ℬ$ be two [[../Cod/|categories]] and

let $F:𝒜\to ℬ$ be a [[../TrivialGroupoid/|functor]]. $F$ is said to be a fully faithful functor if it is an [[../IsomorphicObjectsUnderAnIsomorphism/|isomorphism]] on every set $Hom(-,-)$ of [[../TrivialGroupoid/|morphisms]], and that it is essentially [[../BCConjecture/|surjective]] if for every [[../TrivialGroupoid/|object]] $X\in ℬ$, there is some $Y\in 𝒜$ such that $X$ and $F(Y)$ are isomorphic.