Stacks on stratified space

In this paper, we go into the study of the 2-category SSS_\Sigma of \Sigma-constructible stacks. The notions of constructible stack was introduced by D. Treumann. It is a natural generalization of constructible sheaf. D. Treumann has also introduced the exit-path 2-category, which is a stratified version of the fundamental 2-groupoid and he has showed that these two 2-categories are equivalent. Our approach is different. We show the 2-equivalence between SSS_\Sigma and a 2-category whose objects are combinatoric data of 2-representations, functors of 2-representations and isomorphisms of functors.