Fr\'echet Lie algebroids and their cohomology

We define Lie and Courant algebroids on Fr'{e}chet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Fr'{e}chet manifold and show that it inherits a Fr'{e}chet Lie algebroid structure. We show that the Lie algebroid cohomology of the $\text{bb}$-cotangent bundle Lie algebroid of a weakly symplectic Fr'{e}chet manifold $M$ is the Lichnerowicz-Poisson cohomology of $M$.