Tensor product of sheaves ($\mathcal{F}{\otimes }_{{\mathcal{O}}_X}\mathcal{G}$)

The tensor product of two sheaves of ${\mathcal{O}}_X$-modules is the sheafification of $U\mapsto \mathcal{F}(U){\otimes }_{{\mathcal{O}}_X(U)}\mathcal{G}(U)$. Its stalk at $x$ is ${\mathcal{F}}_x{\otimes }_{{\mathcal{O}}_{X,x}}{\mathcal{G}}_x$.