topos-adhesive-rewriting

Adhesive-category rewriting enables incremental query updating by precomputing decompositions Q ≅ Q_G +_{Q_L} Q_R and reusing partial results when inputs change, avoiding full recomputation of pattern matches and rule applications.

Pattern matching in adhesive categories uses pushouts along monomorphisms to guarantee well-behaved rule application. This ensures decompositions into common elements, matches, and complements remain consistent during incremental updates across graphs and C-set structures.

Yes. Adhesive-category rewriting converts subgraph isomorphism into rooted search problems and enumerates interactions between patterns and rewrite rules using pullback squares, enabling efficient boundary optimization with complements.

Adhesive-category rewriting applies to graphs, C-set-like structures, and any domain where pushouts along monomorphisms preserve decomposition properties, supporting pattern matching and incremental rule application across these structures.

The Skill extends partial matches to full matches by leveraging pullbacks and pushouts within the adhesive-category framework, systematically enumerating how query elements align with rule patterns and incrementally refining results.

Precomputing all decompositions Q ≅ Q_G +_{Q_L} Q_R eliminates recomputation when queries or rules change. Incremental updates recalculate only affected portions, reducing complexity for large-scale graph pattern matching and rule application workflows.