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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開発者ツール

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

概要

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.

主な機能

Mate correspondence and hom-set bijection generation
2 GitHub stars
Unit and counit natural transformation synthesis
Universal construction generation for limits, colimits, and monads
Automated verification of triangle identities and coherence conditions
Directed type theory integration for ∞-categorical structures

ユースケース

Synthesizing monads and comonads from fundamental adjunction data
Formally verifying free-forgetful adjunctions in algebraic structures
Generating Kan extensions as left or right adjoints to restriction functors

概要

主な機能

Mate correspondence and hom-set bijection generation
2 GitHub stars
Unit and counit natural transformation synthesis
Universal construction generation for limits, colimits, and monads
Automated verification of triangle identities and coherence conditions
Directed type theory integration for ∞-categorical structures

ユースケース

Synthesizing monads and comonads from fundamental adjunction data
Formally verifying free-forgetful adjunctions in algebraic structures
Generating Kan extensions as left or right adjoints to restriction functors