Formalize Segal-type structures for synthetic infinity-categories in Lean4, Agda, and InfinityCosmos.
npx skills add https://github.com/plurigrid/asi --skill segal-types
Please help me install this Agent Skill. Skill: segal-types Source: https://github.com/plurigrid/asi/tree/main/skills/segal-types Command: npx skills add https://github.com/plurigrid/asi --skill segal-types
Provides Segal-type formalism for synthetic ∞-categories, ensuring coherent composition across all dimensions.
Open a Lean4/InfinityCosmos workspace and paste the Segal-type definitions to experiment with coherent composition.
High-intent search queries and answers about installing and using this skill.
Segal-type coherence validation ensures binary composites are uniquely defined across all dimensions in synthetic ∞-categories. The formalism resolves composition through directed intervals, hom types, 2-simplices, and Segal conditions, guaranteeing coherent associativity and unitality in type-theory environments like Lean4, Agda, and Rzk.
A Segal space formalizes higher-categorical structure by encoding objects, 1-morphisms, and 2-morphisms with composition witnesses that satisfy Segal conditions at every dimension. This approach bridges synthetic type theory with ∞-categorical semantics, enabling coherent composition proofs without explicit associativity or unitality specifications.
Yes. Segal-type definitions integrate directly into Lean4, Agda, Rzk, and InfinityCosmos tooling. Paste the formal definitions into your workspace to experiment with coherent composition and construct objects and morphisms across all categorical dimensions.
The Segal-type wrapper guarantees coherent associativity and unitality by wrapping composition witnesses and hom types. It eliminates manual proof overhead for composition uniqueness, allowing type checkers to verify coherence automatically across all dimensions in synthetic ∞-categories.
Segal-type formalism targets researchers and educators working in type-theory environments. Familiarity with Lean4, Agda, or related proof assistants, plus basic ∞-categorical concepts, enables effective use. The formalism is designed for advanced category-theory applications in formal mathematics.
Segal conditions constrain hom types and 2-simplices to enforce that composition respects coherence at every dimension. Combined with directed intervals and composition witnesses, they ensure binary composites remain unique and associative-unital without redundant axioms.
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