  We study representations of hemistrict Lie 2-algebras and give a functorial
construction of their cohomology. We prove that both the cohomology of an
injective hemistrict Lie 2-algebra $L$ and the cohomology of the semistrict Lie
2-algebra obtained from skew-symmetrization of $L$ are isomorphic to the
Chevalley-Eilenberg cohomology of the induced Lie algebra
$L_{\operatorname{Lie}}$.
