  We analyze higher gauge theories in various dimensions using a supergeometric
method based on a differential graded symplectic manifold, called a
QP-manifold, which is closely related to the BRST-BV formalism in gauge
theories. Extensions of the Lie 2-algebra gauge structure are formulated within
the Lie n-algebra induced by the QP-structure. We find that in 5 and 6
dimensions there are special extensions of the gauge algebra. In these cases, a
restriction of the gauge symmetry by imposing constraints on the auxiliary
gauge fields leads to a covariantized theory. As an example we show that we can
obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is
similar to the one proposed in [1] (arxiv:1206.5643).
