  We introduce a notion of strong closing property of contact forms, inspired
by the $C^\infty$ closing lemma for Reeb flows in dimension three. We then
prove a sufficient criterion for strong closing property, which is formulated
by considering a monoidal functor from a category of manifolds with contact
forms to a category of filtered vector spaces. As a potential application of
this criterion, we propose a conjecture which says that a standard contact form
on the boundary of any symplectic ellipsoid satisfies strong closing property.
