Compute naturality factors for functor transformations across conserved quantities.
npx skills add https://github.com/plurigrid/asi --skill naturality-factor
Please help me install this Agent Skill. Skill: naturality-factor Source: https://github.com/plurigrid/asi/tree/main/skills/naturality-factor Command: npx skills add https://github.com/plurigrid/asi --skill naturality-factor
Quantifies how well transformations commute with structure, i.e., how natural a transformation is with respect to a given functor and conservation law.
Run a quick naturality check on a transposition or morphism against a target object.
High-intent search queries and answers about installing and using this skill.
Naturality measures how well a transformation commutes with functor structure. Provide a conservation law, source and target functors, a transformation (eta), a morphism, and objects to compute a numeric naturality factor and defect, determining whether the transformation preserves the conservation.
Yes. The Skill evaluates transpositions, inversions, retrogrades, and Rubato morphisms using GF(3), Chromatic 12Z, and Diatonic conservation frameworks, with specialized chromatic and triadic naturality checks for musical structures.
Naturality supports GF(3), Chromatic 12Z, Diatonic, and Yoneda conservation frameworks. Each applies different structural constraints to evaluate how transformations preserve conservation properties across categorical and musical contexts.
Rubato bridges track natural morphisms alongside standard morphisms, enabling evaluation of transformations that preserve structure under flexible timing or harmonic contexts. The Skill exposes RubatoBridge integration for specialized morphism analysis.
Required inputs are a conservation law, source functor, target functor, transformation (eta), morphism, and objects. The Skill returns a factor, defect, naturality determination, and specialized checks like chromatic or Yoneda conservation results.
Use category theory naturality (Yoneda conservation) for abstract functor transformations; use chromatic or triadic naturality for music-specific analysis. Metadata specifies which conservation framework suits your transformation domain and structural constraints.
BellaBeGenerate Lean 4 proofs for categorical laws and verification reports.
EpiphyticValidate analysis results for data quality, calculation accuracy, and reporting reliability.
parcadeiVerify naturality and analyze components of natural transformations in Lean 4.
parcadeiVerify category axioms and functor properties using Lean 4.
