A current on an open subset $W$ of ${X^{\rm an}}$ is a linear functional $T$ on $A_{c}^{p,q}(W)$ such that the restriction of $T$ to all subspaces $A^{p,q}(V_{i},U_{i},\Delta_{i}:i\in I)$ is continuous. The space of currents is a $C^{\infty}(W)$-module denoted by $D_{p,q}(W)$. As usual, we define the differential operators $d^{\prime}$, $d^{\prime\prime}$ and $d:=d^{\prime}+d^{\prime\prime}$ on the total space of currents $D(W):=\bigoplus_{p,q}D_{p,q}(W)$. Using partitions of unity from Proposition 5.10, it is easy to show that the currents form a sheaf on ${X^{\rm an}}$.