Which formal languages is this skill compatible with?

It is specifically designed for directed type theory environments, including Narya and Rzk-based formalizations of synthetic ∞-categories.

Can this skill help with cocartesian lifts?

Yes, it provides automated commands to compute and generate cocartesian lifts, characterizing the existence of transport within a fibration.

What are covariant fibrations in this context?

Covariant fibrations are type families where transport follows the direction of morphisms, essential for modeling non-invertible paths in directed type theory.

How does it handle the Segal condition?

The skill validates that composition witnesses in your types satisfy the Segal condition, ensuring they behave as proper ∞-categories.

What does the 'Trit -1' status signify?

A Trit of -1 indicates this skill acts as a validator or constraint, ensuring that your code or proof maintains covariance and respects directed interval properties.

Covariant Fibrations & Directed Transport

Name: Covariant Fibrations & Directed Transport
Author: plurigrid

byplurigrid

•

Security & Testing

Validates and automates Riehl-Shulman covariant fibrations for directed type theory within synthetic infinity-categories.

The Covariant Fibrations skill is a specialized tool for formal methods and category theory, specifically designed to handle type families that respect directed morphisms. It provides the necessary logic to manage transport along the directed interval, verify Segal conditions, and compute cocartesian lifts. This skill is essential for researchers and developers working with Narya-style directed type theory or Rzk, allowing for the rigorous modeling of non-invertible transformations and directed transport in complex topological computing environments.

Key Features

017 GitHub stars

02Support for Segal type validation in ∞-category formalizations

03Integration with GF(3) triad logic for topological systems

04Automated computation of cocartesian lifts from base morphisms

05Validation of covariance conditions for dependent type families

06Generation of transport terms along the directed interval (0 → 1)

Use Cases

01Modeling directed state transitions in topological chemputer architectures

02Verifying functoriality and composition in directed type systems

03Formalizing synthetic infinity-categories in Rzk or Narya-style languages

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi covariant-fibrations

For use in Claude.ai and ChatGPT

Download Skill