  This paper provides an alternative, much simpler, definition for Li-Bland's
LA-Courant algebroids, or Poisson Lie 2-algebroids, in terms of split Lie
2-algebroids and self-dual 2-representations. This definition generalises in a
precise sense the characterisation of (decomposed) double Lie algebroids via
matched pairs of 2-representations. We use the known geometric examples of
LA-Courant algebroids in order to provide new examples of Poisson Lie
2-algebroids, and we explain in this general context Roytenberg's equivalence
of Courant algebroids with symplectic Lie 2-algebroids. We study further the
core of an LA-Courant algebroid and we prove that it carries an induced
degenerate Courant algebroid structure. In the nondegenerate case, this gives a
new construction of a Courant algebroid from the corresponding symplectic Lie
2-algebroid. Finally we completely characterise VB-Dirac and LA-Dirac
structures via simpler objects, that we compare to Li-Bland's pseudo-Dirac
structures.
