We first define the concept of Lie algebroid in convenient setting. In reference to finite dimensional context, we adapt notion prolongation a over fibred manifold manifold. Then show that this construction is stable under projective and direct limits adequate assumptions.

We associate Hamiltonian homological evolutionary vector fields --which are the non-Abelian variational Lie algebroids' differentials-- with algebra-valued zero-curvature representations for partial differential equations.

We develop the Palatini formalism within framework of generalized Riemannian geometry Courant algebroids. In this context, variation a Einstein–Hilbert–Palatini action - formed using metric, algebroid connection (in contrary to ordinary case, not necessarily torsionless one) and volume form leads naturally proper notion Levi-Civita low-energy effective actions string theory.