Lagrangian cobordism functor in microlocal sheaf theory I

Given a Lagrangian cobordism $L$ of Legendrian submanifolds from $Λ_-$ to $Λ_+$, we construct a functor $Φ_L^*: Sh^c_{Λ_+}(M) \rightarrow Sh^c_{Λ_-}(M) \otimes_{C_{-*}(Ω_*Λ_-)} C_{-*}(Ω_*L)$ between sheaf categories of compact objects with singular support on $Λ_\pm$ and its right adjoint on sheaf c