Classification of Constructible Cosheaves
Abstract
In this paper we prove an equivalence theorem originally observed by Robert MacPherson. On one side of the equivalence is the category of cosheaves that are constructible with respect to a locally cone-like stratification. Our constructibility condition is new and only requires that certain inclusions of open sets are sent to isomorphisms. On the other side of the equivalence is the category of functors from the entrance path category, which has points for objects and certain homotopy classes of paths for morphisms. When our constructible cosheaves are valued in we prove an additional equivalence with the category of stratified coverings.
Cite
@article{arxiv.1603.01587,
title = {Classification of Constructible Cosheaves},
author = {Justin Curry and Amit Patel},
journal= {arXiv preprint arXiv:1603.01587},
year = {2021}
}
Comments
Version 6 is the final, accepted, and published version in TAC. Section 8 of v5 on simplicial refinements has been removed from v6. The main theorem of that section, Theorem 8.8, had a gap in its proof