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

•

开发者工具

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

关于

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.

主要功能

Compute and verify cocartesian lifts for base morphisms
Analyze Segal conditions for ∞-category implementation
Validate covariance conditions within Rzk and Narya-style files
2 GitHub stars
Generate transport terms for directed type families along the interval 𝟚
Integrate with GF(3) triad structures for compositional naturality

使用场景

Implementing directed transport mechanisms in specialized formal languages
Formalizing proofs in synthetic directed homotopy type theory
Developing and verifying synthetic ∞-categories using Rzk

关于

主要功能

Compute and verify cocartesian lifts for base morphisms
Analyze Segal conditions for ∞-category implementation
Validate covariance conditions within Rzk and Narya-style files
2 GitHub stars
Generate transport terms for directed type families along the interval 𝟚
Integrate with GF(3) triad structures for compositional naturality

使用场景

Implementing directed transport mechanisms in specialized formal languages
Formalizing proofs in synthetic directed homotopy type theory
Developing and verifying synthetic ∞-categories using Rzk