What is the connection between Poly and Open Games?

Open games are represented as polynomial coalgebras, where strategy profiles are positions and equilibrium conditions are determined by polynomial morphisms.

Does this skill support the Dialectica interpretation?

Yes, it includes support for Dialectica sets and categories, allowing for proof-relevant semantics and logical modeling within the Poly framework.

How does this skill help with functional programming?

It provides a formal basis for bimorphic lenses and containers, which are crucial for state management and bidirectional data flow in functional languages.

What are polynomial functors used for in software?

Polynomial functors model interactive systems where 'positions' represent states and 'directions' represent available actions or inputs at those states.

Topos Polynomial Functors

Name: Topos Polynomial Functors
Author: plurigrid

byplurigrid

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データサイエンスとML

Models complex interactions and compositional systems using the categorical framework of polynomial functors and dialectica categories.

This skill empowers Claude with specialized knowledge in category theory, specifically focusing on the formalizations of polynomial functors (Poly) and Dialectica categories developed by the Topos Institute. It allows for the rigorous modeling of interactive systems, open games, and data migrations using mathematical concepts like position-direction structures, vertical-cartesian factorization, and sum-product completions (ΣΠC). It is an essential tool for researchers and engineers building compositional software architectures, functional programming lenses, or formal protocol specifications.

主な機能

01Modeling of Open Games as polynomial coalgebras

02Functional programming pattern generation using bimorphic lenses

03Implementation of Dialectica categories (D(Set), G(Set), Gd(C))

04Formalization of Polynomial Functors and ΣΠC completions

05Vertical-Cartesian morphism factorization for system decomposition

068 GitHub stars

ユースケース

01Architecting state-space interactions and database schemas using Poly

02Designing compositional protocols for decentralized systems and game theory

03Formalizing proof-relevant game semantics and interactive logic

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi topos-polynomial-functors

For use in Claude.ai and ChatGPT

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