Categories of Constructible Sheaves

TL;DR

This paper investigates the relationship between derived categories of constructible sheaves and those with constructible cohomology on stratified spaces, establishing foundational properties of these categories.

Contribution

It provides new results on when the functor between these derived categories is an equivalence and clarifies basic properties of locally constant and constructible sheaves.

Findings

The functor from constructible sheaves to sheaves with constructible cohomology can be an equivalence under certain conditions.

Basic properties of locally constant sheaves are established.

Foundational facts about the category of constructible sheaves are clarified.

Abstract

Given a stratified topological space, we answer the question whether the functor from the derived category of constructible sheaves to the derived category of sheaves with constructible cohomology is an equivalence. We also establish basic facts on the category of locally constant sheaves and on the category of constructible sheaves.