Working synthetically in higher categorical structures

这个项目的目的是在高等范畴论的数学学科中开发综合推理的工具。自从引入欧几里得几何以来，综合推理不断地给数学带来革命。该项目希望将这些好处带到重要的新结构中，如（无穷，2）类和一元双类，并建立这些结构的扩展应用圈。该项目的主要成果将是新的科学工具，这将极大地造福于代数拓扑和几何、量子物理和计算机科学等不同应用领域的工作者，同时也有助于培养澳大利亚下一代科学领袖。

This project aims to develop tools for synthetic reasoning in the mathematical discipline of higher category theory. Since its introduction in Euclidean geometry, synthetic reasoning has repeatedly revolutionised mathematics. The project expects to bring these benefits to important new structures such as (infinity, 2)-categories and monoidal bicategories, as well as building the expanding circle of applications of these structures. The project's key outcome will be new scientific tools which will greatly benefit workers in areas of application as diverse as algebraic topology and geometry, quantum physics and computer science, while also helping to train Australia's next generation of scientific leaders.