What is a Galois connection in software engineering?

A Galois connection is a pair of maps between two ordered sets (preorders) that provides a mathematically consistent way to convert data while preserving order, often used to define 'best-fit' approximations like floor and ceiling.

Can this be used for graph analysis?

Yes, it applies Lawvere's derivation of logic to subgraphs, allowing for the calculation of intrinsic boundaries, negations, and complements within complex C-set structures.

How does this skill help with rounding data?

It uses 'adjoint strings' of length 3 to implement lawful rounding behaviors (floor, round-to-nearest, and ceiling) that are guaranteed to be monotonic and consistent across different data types.

What programming languages are supported?

The skill provides implementation patterns primarily for Python and Julia, but the underlying mathematical principles can be applied to any language supporting functional or object-oriented paradigms.

Galois Connections & Adjoint Logic

Name: Galois Connections & Adjoint Logic
Author: plurigrid

byplurigrid

•

开发者工具

Implements mathematically rigorous Galois connections and adjoint pairs for lawful type conversions and categorical logic operations.

This skill enables Claude to apply Category Theory principles—specifically Galois connections—to software engineering tasks involving data transformation and logic. By treating conversions as adjoint pairs, it provides robust implementations for floor, ceiling, and rounding behaviors that preserve preorder properties. It also facilitates Lawvere's derivation of propositional logic within bi-Heyting topos structures, making it an essential tool for developers working on formal verification, high-precision numerical systems, and complex graph-based data models like ACSets and C-sets.

主要功能

01Bi-Heyting algebra operations for advanced subgraph and boundary analysis

02Verified implementation patterns for Python, Julia, and Haskell environments

03Lawful type conversion patterns using floor, ceiling, and middle-adjoint rounding

048 GitHub stars

05Categorical derivation of logical connectives (∧, ∨, ⇒, ¬) via adjunctions

06Adjoint string implementation for banker's rounding and precision analysis

使用场景

01Ensuring mathematical correctness in lossy data conversions between numeric types

02Implementing advanced topological queries and dual negations in graph databases

03Formally verifying that data mapping functions satisfy monotonicity and adjunction laws

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi galois-connections

For use in Claude.ai and ChatGPT

Download Skill