Foundations of higher dimensional homological algebra

高维同调代数基础

• 批准号: DP0558372
• 负责人: A/Prof Michael Batanin
• 金额: $ 10.41万
• 依托单位: Macquarie University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2005
• 资助国家: 澳大利亚
• 起止时间: 2005-03-01 至 2010-03-15
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0558372
• 关键词: Foundations; higher; dimensional; homological; algebra

Recent discoveries in physics and mathematics led to the understanding that classical mathematics is only 'the tip of the iceberg' of the higher-dimensional structures that are ultimately behind the laws of Nature. Australia has always been in the forefront of research in Category Theory, and due to that position, has a unique opportunity to participate in the early stages of developments of Higher Category Theory and Higher Dimensional Homological Algebra. This will allow Australia to be in the forefront of the subsequent technological development and to reap the economical, social and intellectual benefits related to it.

物理学和数学的最新发现使人们认识到，经典数学只是自然规律背后的高维结构的“冰山一角”。澳大利亚一直处于范畴理论研究的前沿，由于这一地位，有一个独特的机会参与高级范畴理论和高维同调代数发展的早期阶段。这将使澳大利亚处于随后技术发展的前沿，并获得与之相关的经济、社会和知识利益。