Working synthetically in higher categorical structures

这个项目旨在开发在高等范畴理论的数学学科中进行合成推理的工具。自欧几里德几何学引入合成推理以来，它一再给数学带来革命性的变化。该项目希望将这些好处带到重要的新结构中，如(无穷大，2)-范畴和一元双范畴，并建立这些结构不断扩大的应用圈。该项目的关键成果将是新的科学工具，这些工具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各种应用领域的工作人员，同时还有助于培养澳大利亚的下一代科学领袖。

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.