Stacks on stratified space

TL;DR

This paper explores the relationship between constructible stacks on stratified spaces and combinatorial data of 2-representations, establishing a new 2-equivalence in the theory of stratified stacks.

Contribution

It introduces a different approach to relating constructible stacks and 2-representations, proving a 2-equivalence that broadens understanding of stratified stack theory.

Findings

Established a 2-equivalence between SSS_Σ and a 2-category of 2-representations

Provided a new approach differing from Treumann's exit-path 2-category

Enhanced the theoretical framework connecting stacks and combinatorial data

Abstract

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.