Theorem: Let $\mathcal{C}$ and $\mathcal{D}$ be categories and let $F:\mathcal{C}\to \mathcal{D}$ be a fully faithful functor. Then $F$ reflects any limits and colimits admitted in the codomain category.
Theorem: Let $\mathcal{C}$ and $\mathcal{D}$ be categories and let $F:\mathcal{C}\to \mathcal{D}$ be a fully faithful functor. Then $F$ reflects any limits and colimits admitted in the codomain category.