build-category

Formalizing a domain as a category involves extracting objects and morphisms from spec artifacts, defining identity morphisms and composition operators, then documenting composition laws. This Skill automates that process by reading spec/objects.yaml and spec/morphisms.yaml, generating a versioned category.yaml artifact with objects, morphisms, identity, composition (pure ∘ and Kleisli >=>), and verification laws.

Pure composition (∘) chains morphisms directly in the category. Kleisli composition (>=>) lifts morphisms through a monad, handling effects or context. This Skill defines both operators so you can express different composition semantics depending on whether your domain morphisms are pure functions or effectful computations.

Category laws — left identity, right identity, and associativity — must hold for all morphism compositions. This Skill captures and documents these laws in the generated artifact, enabling downstream tooling to verify them against your domain's morphisms and composition definitions.

Yes. This Skill reads objects and morphisms from spec YAML files you provide, translating your domain specification into formal category structure. It works with any spec artifact format you've defined in spec/objects.yaml and spec/morphisms.yaml.

This Skill generates a versioned YAML artifact (artifacts/v{N}/build/category.yaml) containing your domain's objects, morphisms, identity definitions, composition operators, and laws. That artifact feeds downstream tooling for analysis, validation, or code generation.

Familiarity with basic category concepts — objects, morphisms, identity, and composition — helps. However, if you're building a domain model with entities and relationships plus rules for how they compose, this Skill formalizes that structure into category notation for precision and verification.