Enriched categories: Applications in geometry and logic

丰富类别：几何和逻辑中的应用

• 批准号: FT160100393
• 负责人: A/Prof Richard Garner
• 金额: $ 56.36万
• 依托单位: Macquarie University
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT160100393
• 关键词: Enriched; categories; Applications; geometry; logic

The project aims to apply enriched categories to fields including algebraic and differential geometry and theoretical computer science. Enriched categories, introduced in Australia in the 1960s, underlie major mathematical results such as Grothendieck’s revolutionary work in algebraic geometry. Emerging scientific areas like higher differential geometry and homotopy type theory urgently need the formalism of enriched categories to be made applicable to them. Success in this could rapidly develop these areas and solidify Australia's position as a leading international force in mathematics.

该项目旨在将丰富的类别应用于包括代数和微分几何以及理论计算机科学在内的领域。丰富的范畴，介绍了在澳大利亚在20世纪60年代，根据主要的数学成果，如格罗滕迪克的革命性工作，代数几何。新兴的科学领域，如高等微分几何和同伦类型理论，迫切需要丰富的范畴的形式主义，使适用于他们。这方面的成功可以迅速发展这些领域，并巩固澳大利亚作为数学领域国际领先力量的地位。