What is the role of a cocartesian lift in this context?

A cocartesian lift allows for the lifting of a morphism from a base category to a fiber category, which is a characterizing property of covariant fibrations.

How does this skill support Segal types?

It provides validation tools for composition witnesses, ensuring that covariant families over Segal types maintain functoriality and composition coherence.

Which formal verification languages are supported?

This skill is designed to assist with directed type theory environments, specifically supporting Narya-style syntax and Rzk-based formalisms.

What are covariant fibrations in directed type theory?

Covariant fibrations are type families where transport follows the direction of morphisms, ensuring that type families correctly propagate along the directed interval.

Covariant Fibrations

Name: Covariant Fibrations
Author: plurigrid

byplurigrid

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Developer Tools

Automates the validation and construction of covariant fibrations for directed type theory and infinity-categorical transport.

The Covariant Fibrations skill implements Riehl-Shulman covariant fibrations to facilitate transport along directed morphisms within synthetic infinity-categories. It provides specialized tools for directed type theory, enabling users to validate covariance conditions, compute cocartesian lifts, and generate transport terms for frameworks like Narya and Rzk. By enforcing the principle that type families respect directed morphisms, this skill ensures compositional coherence across directed intervals and supports the rigorous development of Segal types and synthetic adjunctions.

Key Features

018 GitHub stars

02Check Segal conditions for compositional witnesses in infinity-categories

03Validate covariance conditions for type families over directed intervals

04Compute and verify cocartesian lifts for fibrations

05Generate transport terms between source and target types

06Integrate with GF(3) triad structures for algebraic coherence

Use Cases

01Verifying that type families correctly propagate along directed 2-arrows

02Automating the generation of transport witnesses in directed type theory

03Constructing formal proofs for synthetic infinity-category theory

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