2020/10/13 by Peter J. Haine, Haine, Peter J., Mauro Porta +3
Mathematics · #18F20 #54B40 #55N30 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2010.06473
openalex publication_date 2020/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to explain why the functor that sends a stratified topological space S to the ∞-category of constructible (hyper)sheaves on S with coefficients in a large class of presentable ∞categories is homotopy-invariant. To do this, we first establish a number of results in the unstratified setting, i.e., the setting of locally constant (hyper)sheaves. For example, if X is a locally weakly contractible topological space and E is a presentable ∞-category, then we give a concrete formula for the constant hypersheaf functor E→ Shhyp(X;E). This formula lets us show that the constant hypersheaf functor is a right adjoint, and is fully faithful if X is also weakly contractible. It also lets us prove a general monodromy equivalence and categorical Künneth formula for locally constant hypersheaves.