How does this skill help with formal verification?

The skill provides commands and structural templates to verify ∞-cosmos axioms and adjunction conditions, specifically optimized for the Rzk proof assistant language.

What are comma ∞-categories in this context?

Comma ∞-categories are generalized slice constructions used to define limits, colimits, and Kan extensions within an ∞-cosmos without needing to specify low-level simplicial details.

What is the Riehl-Verity formalism?

It is a model-independent approach to ∞-category theory that focuses on the common properties shared by various models (like quasi-categories or Segal spaces) using the concept of an ∞-cosmos.

Can I use this for specific models like quasi-categories?

Yes, because the framework is model-independent, it applies to any specific model that satisfies the ∞-cosmos axioms, including quasi-categories and complete Segal spaces.

Elements of ∞-Category Theory

Name: Elements of ∞-Category Theory
Author: plurigrid

byplurigrid

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Data Science & ML

Facilitates model-independent ∞-category theory using the Riehl-Verity ∞-cosmos formalism for formal verification and mathematical modeling.

About

This skill provides a foundational framework for reasoning about ∞-categories without committing to a specific model like quasi-categories or complete Segal spaces. By leveraging the ∞-cosmos formalism, it enables Claude to assist in constructing model-independent definitions for adjunctions, limits, and comma constructions. It is particularly valuable for researchers and developers working in synthetic category theory, topological computing, or formal verification using tools like Rzk, ensuring compositional coherence across complex mathematical structures.

Key Features

Integration with synthetic category theory tools like Rzk
Model-independent ∞-cosmos framework implementation
2 GitHub stars
Automated comma ∞-category and slice constructions
Support for isofibrations and factorization systems
Formal verification for adjunctions and equivalences

Use Cases

Constructing model-independent adjunctions between high-dimensional categories
Automating the setup of comma categories for topological computing architectures
Formally verifying mathematical proofs in synthetic ∞-category theory

About

Key Features

Integration with synthetic category theory tools like Rzk
Model-independent ∞-cosmos framework implementation
2 GitHub stars
Automated comma ∞-category and slice constructions
Support for isofibrations and factorization systems
Formal verification for adjunctions and equivalences

Use Cases

Constructing model-independent adjunctions between high-dimensional categories
Automating the setup of comma categories for topological computing architectures
Formally verifying mathematical proofs in synthetic ∞-category theory