2025/12/14 by Bai, Qingyuan, Haine, Peter J.
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2512.12810
Given an open-closed decomposition of the stratifying poset, we construct a new semi-orthogonal decomposition of the ∞-category of constructible sheaves on a stratified space admitting an exit-path ∞-category. From this we obtain a direct sum decomposition of the localizing invariants of the ∞-category of constructible sheaves. Since the ∗-pullback to the open stratum in the usual (recollement) semi-orthogonal decomposition is not strongly left adjoint, this splitting does not follow from pure sheaf theory considerations. Instead, the splitting crucially relies on the exodromy equivalence: it implies that on the level of constructible sheaves, the ∗-pullback to a closed stratum and the !-pushforward from an open stratum admit left adjoints. These new functors provide an additional semi-orthogonal decomposition (with the roles of open and closed reversed) in which the relevant functors are strongly left adjoint.