Let $M$ be a differentiable manifold.
Let $T^*M$ be the cotangent bundle of $M$.
Consider the exterior differentiation $d: A^p(M)\longrightarrow A^{p+1}(M)$, where $A^p(M)=\Gamma(\bigwedge^p T^*M)$, $p=0,1,2,\dotsc$.
Let $L$ be a subbundle of $T^*M$.
Suppose $L$ is a foliation, i.e. for any sections $X,Y\in \Gamma(L)$, we have $[X,Y]\in \Gamma(L)$.
Question.
Whether or not could we have a well-defined exterior differentiation $d: \Gamma(\bigwedge^pL)\longrightarrow \Gamma(\bigwedge^{p+1}L)$?