Invariants of higher-dimensional categories, with applications

高维类别的不变量及其应用

• 批准号: DP0346047
• 负责人: Em/Prof Ross Street
• 金额: $ 15.33万
• 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: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2006-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0346047
• 关键词: Invariants; higher; dimensional; categories; applications

Complex systems in mathematics are difficult to tell apart so one constructs simpler structures from them. These structures must be equal, isomorphic or equivalent when the original systems are equivalent; the word invariant is used for such constructions. Higher-dimensional categories are complex structures that are currently gaining a lot of attention from mathematicians, physicists and computer scientists because of developing applications in those fields. This project will establish and study invariants for higher-dimensional categories which will be tested by examining their viability for producing results in group theory and homotopy theory.

数学中的复杂系统很难区分开来，所以人们可以从它们中构造出更简单的结构。当原始系统等价时，这些结构必须是相等的、同构的或等价的;不变式一词用于这种结构。 高维范畴是一种复杂的结构，由于在这些领域的应用，目前正受到数学家、物理学家和计算机科学家的广泛关注。 这个项目将建立和研究高维范畴的不变量，通过检查它们在群论和同伦理论中产生结果的可行性来测试。