Category embedding

An embedding of a category $𝖢$ in $𝖣$ is a fully faithful functor $𝐼 : 𝖢 ↪ 𝖣$ which is injective on objects. #m/def/cat

It follows that any natural transformation $𝜂 : 𝐼 𝐹 \Rightarrow 𝐼 𝐺$ of embedded objects lifts to a natural transformation $𝐼 - 1 : 𝐹 \Rightarrow 𝐺$ of the objects themselves.