Constructible sheaves on simplicial complexes and Koszul duality

Abstract

We obtain a linear algebra data presentation of the category SHc(X, δ) of sheaves constant along the perverse simplices on a finite simplicial complex X. We also establish Koszul duality between SHc(X, δ) and the category Mc(X, δ) of perverse sheaves constructible with respect to the triangulation.