What is the primary purpose of the Synthetic Adjunctions skill?

It is designed to automate the generation and verification of adjoint functors and universal constructions within directed type theory, specifically for ∞-categorical applications.

Does this skill support formal verification languages?

Yes, it is designed to work with directed type theory environments like Rzk and provides patterns compatible with proof assistants like Agda.

Can I use this to generate monads?

Absolutely. The skill specializes in generating free-forgetful adjunctions, which are the foundational components for constructing algebraic monads.

What are the core components it generates?

It generates unit and counit transformations (η and ε), checks triangle identities, and characterizes universal arrows and Kan extensions.

Synthetic Adjunctions

Name: Synthetic Adjunctions
Author: plurigrid

byplurigrid

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Developer Tools

Synthesizes and verifies universal constructions using directed type theory for advanced categorical programming and formal verification.

The Synthetic Adjunctions skill provides a specialized framework for generating and validating adjunction data within directed type theory, specifically for ∞-categorical applications. It automates the creation of fundamental mathematical structures including unit/counit pairs, triangle identities, and Kan extensions, facilitating the implementation of limits, colimits, and monads. This tool is particularly useful for developers and researchers working on formal methods, topological computing, or high-level functional programming who require rigorous coherence in their universal constructions.

Key Features

01Verification of mate correspondence and universal properties

02Generation of free-forgetful adjunctions from monadic structures

037 GitHub stars

04Automatic generation of unit (η) and counit (ε) natural transformations

05Formal synthesis of triangle identities and coherence conditions

06Construction of Kan extensions as adjoint functors

Use Cases

01Formalizing ∞-categorical structures in Rzk or Agda environments

02Generating boilerplate for monad-based programming language semantics

03Verifying the mathematical correctness of topological chemputer models

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