What is an ∞-Topos?

An ∞-Topos is an (∞,1)-category that generalizes the notion of a Grothendieck topos, satisfying specific axioms like colimit completeness, descent, and the existence of object classifiers.

What is the connection between GA and ∞-Topos?

The skill models Geometric Algebra central extensions as fiber sequences and uses cohomology within ∞-topoi to classify grade filtration extensions.

How does this skill assist with Lean 4?

It provides specialized templates and structural guidance for formalizing ∞-categorical theorems, specifically leveraging libraries like infinity-cosmos for theorem proving.

Which mathematical foundations are supported?

The skill is grounded in Jacob Lurie's 'Higher Topos Theory', Rezk's homotopy toposes, and the Riehl-Verity framework for ∞-category theory.

Can I use this for data modeling in Julia?

Yes, it includes ACSet (Attributed C-Set) schemas for Catlab.jl to represent n-morphisms, universal properties, and composition within a topological framework.

Infinity Topos Theory

Name: Infinity Topos Theory
Author: plurigrid

byplurigrid

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数据科学与机器学习

Facilitates advanced (∞,1)-category theory modeling, Lean 4 formalization, and Geometric Algebra extensions.

This skill empowers Claude to navigate and implement complex (∞,1)-topos structures, bridging the gap between higher category theory and Geometric Algebra (GA). It provides specialized knowledge for working with Lurie's characterizations, Giraud's axioms, and Lean 4 ∞-cosmos foundations. Users can leverage this skill to model abelian extensions, manage hatchery repositories for topological computing, and utilize ACSet schemas for categorical data representation within the context of the 'topological chemputer' framework.

主要功能

018 GitHub stars

02Integration with hatchery repositories for topological system development

03Formalization of ∞-Topos theory using Lurie's Giraud axioms

04Bridge between Geometric Algebra (GA) and ∞-topos abelian extensions

05Julia/Catlab ACSet schema definitions for higher category objects

06Lean 4 code generation for ∞-category and ∞-cosmos structures

使用场景

01Modeling complex grade filtrations in Geometric Algebra as fiber sequences

02Designing schema-based topological data structures for advanced research applications

03Formalizing higher categorical proofs and structures in Lean 4

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi infinity-topos

For use in Claude.ai and ChatGPT

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