Criteria for presheaf presentations of constructible sheaf categories with singular support

Characterize the precise conditions under which the category of constructible sheaves with prescribed singular support on a stratified manifold admits a presentation as a presheaf category on an explicit quiver with relations; identify necessary and sufficient geometric or combinatorial criteria on the conic Lagrangian and the stratification for such an algebraic description to exist.

Background

The paper demonstrates examples (e.g., projective spaces) where quasi-coherent sheaves are modeled by presheaf categories on quivers, and raises the prospect of similar descriptions for constructible sheaves with singular support constraints. However, such presentations are not universally available.

Understanding when sheaf categories with singular support constraints admit presheaf (quiver) descriptions would bridge microlocal sheaf theory with explicit algebraic models and clarify the scope of tractable computations in mirror symmetry contexts.