Which formal languages does this skill support?

It primarily targets proof assistants and formal languages used for category theory, specifically Rzk and Agda.

What is a synthetic adjunction?

A synthetic adjunction is an adjunction formulated within directed type theory, allowing for the formal synthesis of universal properties and coherence conditions in higher category theory.

Can it verify triangle identities?

Yes, the skill includes commands to verify that generated unit and counit pairs satisfy the necessary coherence conditions for a valid adjunction.

How does it handle Kan extensions?

It treats Kan extensions as specific types of adjunctions—specifically as left or right adjoints to restriction functors—allowing for automated generation and verification.

Synthetic Adjunctions Generator

Name: Synthetic Adjunctions Generator
Author: plurigrid

byplurigrid

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Developer Tools

Automates the generation of universal constructions and adjoint functors within directed type theory frameworks.

Synthetic Adjunctions is a specialized tool for developers and mathematicians working in ∞-category theory and directed type theory. It provides a structured way to synthesize unit-counit pairs, verify triangle identities, and generate universal structures like limits, colimits, and Kan extensions. By automating the complex boilerplate of formal adjunctions, it enables Claude to assist in rigorous mathematical modeling and formal verification tasks using proof assistants like Rzk and Agda.

Key Features

01Mate correspondence and hom-set bijection generation

022 GitHub stars

03Unit and counit natural transformation synthesis

04Universal construction generation for limits, colimits, and monads

05Automated verification of triangle identities and coherence conditions

06Directed type theory integration for ∞-categorical structures

Use Cases

01Synthesizing monads and comonads from fundamental adjunction data

02Formally verifying free-forgetful adjunctions in algebraic structures

03Generating Kan extensions as left or right adjoints to restriction functors

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi synthetic-adjunctions

For use in Claude.ai and ChatGPT

Download Skill