Monoidal categories and beyond: new contexts and new applications

幺半群范畴及其他：新上下文和新应用

• 批准号: DP160101519
• 负责人: Em/Prof Ross Street
• 金额: $ 40.52万
• 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: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-06-30 至 2019-06-17
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP160101519
• 关键词: Monoidal; categories; beyond; new; contexts

The project aims to develop a theory of generalised monoidal structures with applications to fields as diverse as combinatorics, representation theory, algebraic geometry, topology, theoretical physics and computer science. Monoidal categories are a mathematical formalism for systems with operations of parallel and serial composition, such as the Hilbert space model of quantum mechanics. Recent developments in topology and quantum algebra have led to more general notions of monoidal category, and further progress requires a comprehensive theory of such structures.

该项目旨在发展一种广义幺半群结构理论，应用于组合数学、表示论、代数几何、拓扑、理论物理和计算机科学等多个领域。幺半群范畴是具有并行和串行组合操作的系统的数学形式，例如量子力学的希尔伯特空间模型。拓扑学和量子代数的最新发展带来了更普遍的幺半群范畴概念，进一步的进展需要此类结构的综合理论。