A New Approach to Defining Cochain Complexes for dual Leibniz algebra

We construct a cochain map embedding the cohomology complex of any dual Leibniz algebra $B$ into the Lie algebra cochain complex of $\mathfrak{g}\otimes B$, where $\mathfrak{g}$ is a Leibniz algebra. This reduces the study of dual Leibniz cohomology to classical Lie algebra cohomology, yielding computational simplifications and new structural insights.