 }:\mathcal{A}lt_{\mathbb{R}}^{\bullet }\left( \Gamma \left( A\right) ;\Gamma \left( \func{End}E\right) \right) \longrightarrow \mathcal{A}lt_{\mathbb{R}}^{\bullet }\left( \Gamma \left( A\right) ;\mathscr{C}^{\infty }\left( M\right) \right)$$