Stacks on stratified space

2010/03/22 by Dupont, Delphine
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1003.4236

Abstract

In this paper, we go into the study of the 2-category SSS_Σof Σ-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_Σand a 2-category whose objects are combinatoric data of 2-representations, functors of 2-representations and isomorphisms of functors.

Related

• Exit paths and constructible stacks
• Exemples de classification du champ des faisceaux pervers
• Constructible hypersheaves via exit paths
• 2-classifiers via dense generators and Hofmann-Streicher universe in stacks
• Stacks similar to the stack of perverse sheaves