Monoidal categories and beyond: new contexts and new applications

该项目旨在发展广义一元结构理论，并将其应用于组合学、表示理论、代数几何、拓扑学、理论物理和计算机科学等领域。一元范畴是具有并行和串行组合操作的系统的数学形式，如量子力学的希尔伯特空间模型。最近拓扑学和量子代数的发展导致了单一型范畴的更一般的概念，进一步的发展需要对这种结构的综合理论。

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.