What is an ∞-cosmos in this context?

An ∞-cosmos is an enriched category of ∞-categories that provides a framework for model-independent reasoning, allowing you to define concepts like adjunctions and limits that work across all models of ∞-categories.

Does this skill require knowledge of specific models like quasi-categories?

No, the primary advantage of this skill is its model-independence; it uses axioms that apply to quasi-categories, complete Segal spaces, and iterated Segal spaces simultaneously.

How does it assist with formal verification?

It provides commands to verify ∞-cosmos axioms and check adjunction conditions, often integrating with tools like Rzk to ensure mathematical proofs are sound.

What are comma ∞-categories used for?

Comma constructions are essential for building slice categories and analyzing the relationships between different morphisms within an ∞-categorical framework.

Infinity Category Foundations

Name: Infinity Category Foundations
Author: plurigrid

byplurigrid

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Developer Tools

Provides model-independent foundations for ∞-category theory based on the Riehl-Verity ∞-cosmos axiomatic framework.

This skill implements foundational constructions for infinity-category theory, enabling developers and mathematicians to work with categories, functors, and adjunctions without being tied to a specific model like quasi-categories or complete Segal spaces. Utilizing the ∞-cosmos formalism, it provides a high-level, axiomatic approach to formal verification and topological computation, offering tools to verify structure, compute comma categories, and check adjunction conditions within a unified framework.

Key Features

01Formal verification of model-independent adjunctions and equivalences

02Integration with Rzk and GF(3) triad structures for topological systems

03Automated computation of comma ∞-categories and slice constructions

047 GitHub stars

05Support for isofibrations and factorization system logic

06Model-independent ∞-cosmos axiomatic framework for categorical reasoning

Use Cases

01Verifying complex adjunctions and fibrations in formal type systems

02Formalizing synthetic ∞-category theory proofs and definitions

03Designing model-agnostic categorical data structures for topological computing

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi elements-infinity-cats

For use in Claude.ai and ChatGPT

Download Skill