Precise formulation of the sheaf–cosheaf duality

Characterize precisely the ways in which cosheaves are dual-analogous to sheaves, including a rigorous formulation of the informal duality between their axioms and categorical properties.

Background

The paper develops cosheaves as dual analogues of sheaves and compares their axioms, character modules, finite-covering behavior, and categorical constructions. It then explicitly asks how this informal duality can be made precise, indicating an unresolved conceptual problem rather than proving a complete formal duality theory.

References

In what ways can one make this informal statement precise?

— The contraherent version of the theorem of Slavik and Stovicek  (2609.08491 - Positselski, 8 Sep 2026) in Remarks, subsection “Locally contraherent cosheaves”