If $N^{\prime}$ is a free abelian group of rank $r^{\prime}$ and if $F:N^{\prime}_{\mathbb{R}}\rightarrow N_{\mathbb{R}}$ is an affine map with $F(V)\subset U$ for an open subset $V$ of $N^{\prime}_{\mathbb{R}}$, then we have a well-defined pull-back $F^{*}:A^{p,q}(U)\rightarrow A^{p,q}(V)$ given as usual. The affine pull-back commutes with the differential operators $d$, $d^{\prime}$ and $d^{\prime\prime}$.