Invariants of higher-dimensional categories, with applications

在数学中，复杂的系统是很难区分的，所以人们用它们来构造更简单的结构。当原始系统相等时，这些结构必须相等、同构或相等；“不变量”一词用于这样的结构。高维类别是复杂的结构，由于在这些领域的应用开发，目前正获得数学家、物理学家和计算机科学家的大量关注。这个项目将建立和研究高维范畴的不变量，这些不变量将通过检验它们在群论和同伦理论中产生结果的可行性来进行测试。

Complex systems in mathematics are difficult to tell apart so one constructs simpler structures from them. These structures must be equal, isomorphic or equivalent when the original systems are equivalent; the word invariant is used for such constructions. Higher-dimensional categories are complex structures that are currently gaining a lot of attention from mathematicians, physicists and computer scientists because of developing applications in those fields. This project will establish and study invariants for higher-dimensional categories which will be tested by examining their viability for producing results in group theory and homotopy theory.