sheaf-cohomology

Čech cohomology verifies local-to-global consistency by computing H⁰, H¹, and H² cohomology groups to detect cocycle obstructions where patches fail to merge. Use tree-sitter to parse AST-level patches, construct the nerve of your code cover, check descent conditions, and validate that local sections glue into a single global section without conflicts.

Čech cohomology is a mathematical framework that studies how local data patches combine globally. Use it when refactoring multi-module systems or integrating schemas across patch boundaries to ensure type compatibility and structural consistency are preserved during gluing operations.

Yes. Tree-sitter parses code structure into ASTs; Čech cohomology validates that AST patches satisfy cocycle and descent conditions. This combination detects integration failures where schema patches conflict, enabling safe schema refactoring and cross-module type alignment.

Build the nerve by mapping your code patches as vertices and their overlaps as edges. Compute Čech cohomology on this nerve to verify descent: check that sections defined locally on patch intersections extend consistently to a global section, confirming patches glue without obstruction.

Cocycle obstructions signal that local patches are mutually inconsistent and cannot merge into a global structure. Čech cohomology H¹ computations expose these obstructions explicitly, allowing you to diagnose incompatibilities in type definitions, schema overlaps, or transition rules before committing changes.

The Skill handles formal cohomology computation; you supply patches, overlaps, and compatibility rules. Understanding basic gluing concepts—how patches intersect and must agree on overlaps—is sufficient to use descent verification and nerve construction for multi-module validation.