  Given a reductive group scheme $G$, we give a linear algebraic description of
reduced \'etale $4$-cocycles on its classifying stack $\mathrm B(G)$. These
cocycles form a $2$-groupoid, which we interpret as parameters of metaplectic
covers of $G$. We use our linear algebraic description to define the Langlands
dual of a metaplectic cover.
