Working synthetically in higher categorical structures

Synthetic approaches to mathematics began in Euclidean geometry. This project aims to develop synthetic approaches to reasoning in higher categorical structures such as (infinity,2)-categories and monoidal bicategories, as well as building on the expanding circle of applications of these structures. The team consists of four world leaders in the technically demanding area of higher categories; their synthetic approach is designed to alleviate these considerable technical demands. Success in this would allow for rapid further development in areas of application as diverse as algebraic topology, algebraic geometry, quantum physics, and computer science, and would solidify Australia's position as a leading international force in mathematics.