  Let $L$ be an exact Lagrangian submanifold of a cotangent bundle $T^* M$,
asymptotic to a Legendrian submanifold $\Lambda \subset T^{\infty} M$. We study
a locally constant sheaf of $\infty$-categories on $L$, called the sheaf of
brane structures or $\mathrm{Brane}_L$. Its fiber is the $\infty$-category of
spectra, and we construct a Hamiltonian invariant, fully faithful functor from
$\Gamma(L,\mathrm{Brane}_L)$ to the $\infty$-category of sheaves of spectra on
$M$ with singular support in $\Lambda$.
