Topological exodromy with coefficients

Abstract

The exodromy equivalence relates the derived $\infty$-category of constructible sheaves on a stratified space (X,P) with the $\infty$-category of representations of the exit-paths $\infty$-category of (X,P). Originally envisioned by MacPherson, it has been rigorously developed by Treumann and later improved by Lurie. This paper provides a new proof of the strongest version of this equivalence. This allows us to remove several limitations from Lurie's treatement; for instance we prove that the exodromy equivalence is functorial in arbitrary morphism of stratified spaces. We also remove all noetherianity assumptions, consider more general coefficients (e.g. compactly assembled or stable presentable $\infty$-categories), and we allow stratified spaces that have locally weakly contractible strata, rather than being locally of singular shape.

64 pages, comments very welcome ! v2: change of coefficients discussions expanded. The applications to cohomological Hall algebras and derived moduli of perverse sheaves will appear in separate papers