Monoidal categories and beyond: new contexts and new applications

该项目旨在开发一种广义单面结构理论，应用于组合学、表示论、代数几何、拓扑学、理论物理和计算机科学等多个领域。单形范畴是具有并行和串联组合运算的系统的数学形式，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导致了么半范畴的更一般的概念，而进一步的进展需要对这种结构的全面理论。

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.