What are covariant fibrations in directed type theory?

Covariant fibrations are type families where transport follows the direction of morphisms, ensuring that information propagates correctly along the directed interval (0 → 1) without requiring invertibility.

What is the significance of the -1 Trit (validator) status?

As a validator/constraint skill, it functions as a safeguard that ensures mathematical structures follow the specific directed rules and Segal conditions required for ∞-category coherence.

Does this skill help with Segal types?

Yes, it includes logic for validating Segal conditions, which provide the composition witnesses necessary for defining categories in a synthetic setting.

How does this skill support Rzk development?

It provides specific commands and logic to check covariance conditions and generate necessary transport terms in .rzk files, automating the repetitive parts of formal category theory proofs.

Covariant Fibrations

Name: Covariant Fibrations
Author: plurigrid

byplurigrid

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開発者ツール

Validates and manages Riehl-Shulman covariant fibrations for directed type theory and synthetic homotopy theory.

The Covariant Fibrations skill provides Claude with specialized capabilities for handling directed transport and type families within the context of Riehl-Shulman fibrations. It is specifically designed for developers and researchers working with directed type theory (Narya-style) and the Rzk language to model ∞-categories. This skill enables the automated validation of covariance conditions, computation of cocartesian lifts, and generation of transport terms, ensuring that type families correctly propagate along the directed interval while maintaining compositional coherence.

主な機能

01Compute and verify cocartesian lifts for base morphisms

02Analyze Segal conditions for ∞-category implementation

03Validate covariance conditions within Rzk and Narya-style files

042 GitHub stars

05Generate transport terms for directed type families along the interval 𝟚

06Integrate with GF(3) triad structures for compositional naturality

ユースケース

01Implementing directed transport mechanisms in specialized formal languages

02Formalizing proofs in synthetic directed homotopy type theory

03Developing and verifying synthetic ∞-categories using Rzk

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi covariant-fibrations

For use in Claude.ai and ChatGPT

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