In the article "Lie theory and the Chern-Weil homomorphism" of A. Alekseev and Meinrenken on page 8 you have the following definition:
2.8.Homotopy operators. The space $L\left ( E,{E}' \right )$ of linear maps $\phi :E\rightarrow {E}'$ between differential spaces is itself a differential space, with differential $d\left ( \phi \right )=d\circ \phi -\left ( -1 \right )^{\left | \phi \right |}\phi \circ d$. Chain maps correspond to cocycles in $L\left ( E,{E}' \right )^{\overline{0}}$.
A homotopy operator between two chains maps $\phi _{0},\phi _{1}:E\rightarrow {E}'$ is an odd linear map $h\in L\left ( E,{E}' \right )^{\overline{1}}$ such that $d\left ( h \right )=\phi _{0}-\phi _{1}$.
Taking into account the definition given on page 6 of the same article:
2.5. A differential space (ds) is a super vector space $E$, together with a differential,i.e. an odd endomorphism $d\in End\left ( E \right )^{\overline{1}}$ satisfying $d\circ d=0$.
So $L\left ( E,{E}' \right )$ is a differential space, together with a odd endomorphism $d\in End(L\left ( E,{E}' \right )^{\overline{1}})$ satisfying $d\circ d=0$.
I want to know in which part of the definition 2.5 works
$d\left ( \phi \right )=d\circ \phi -\left ( -1 \right )^{\left | \phi \right |}\phi \circ d$. Chain maps correspond to cocycles in $L\left ( E,{E}' \right )^{\overline{0}}$.
Thanks for the help