Enriched categories: Applications in geometry and logic

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。20世纪60年代在澳大利亚引入的丰富范畴是主要数学成果的基础，例如格罗滕迪克在代数几何方面的革命性工作。高等微分几何和同伦型论等新兴科学领域迫切需要丰富范畴的形式主义应用于它们。这方面的成功可以迅速发展这些领域，巩固澳大利亚作为国际数学领先力量的地位。

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.