Let $X$ be a topological space and $\mathcal{F}$ be a presheaf on $X$. We denote by $\mathcal{F}^+$ the sheafification of $\mathcal{F}$.
Let $U\subset X$ be an open subset. We denote by $\mathcal{F}|_U$ the presheaf given by $\mathcal{F}|_U(V)=\mathcal{F}(U\cap V)$. How I can prove the isomorphism $\mathcal{F}^+|_U \simeq \mathcal{F}|_U^+$ in a clean way? without recalling the definitions?
Thanks in advance.