  The gauge symmetry and shift/translational symmetry of a 3D BF action, which
are associated to a pair of dual Lie algebras, can be combined to form the
Drinfel'd double. This combined symmetry is the gauge symmetry of the
Chern-Simons action which is equivalent to the BF action, up to some boundary
term. We show that something similar happens in 4D when considering a 2-BF
action (aka BFCG action), whose symmetries are specified in terms of a pair of
dual strict Lie 2-algebras (ie. crossed-modules). Combining these symmetries
gives rise to a 2-Drinfel'd double which becomes the gauge symmetry structure
of a 4D BF theory, up to a boundary term. Concretely, we show how using 2-gauge
transformations based on dual crossed-modules, the notion of 2-Drinfel'd double
defined in Ref. arXiv:1109.1344 appears. We also discuss how, similarly to the
Lie algebra case, the symmetric contribution of the $r$-matrix of the
2-Drinfel'd double can be interpreted as a quadratic 2-Casimir, which allows to
recover the notion of duality.
