Abstract: From a fixed symplectic cohomology class $\Gamma \in SH^\bullet(M)$ of a Liouville manifold $M$, we construct a new $A_\infty$ category denoted by $Cone(\Gamma)$ on which the quantum cap action of $\Gamma\cap : CW^\bullet(L, L) \to CW^\bullet(L,L)$ vanishes. We also present a cohomology level description of this category. In addition, on the homological mirror symmetry, this construction corresponds to a restricting Landau-Ginzburg model to its hypersurface.