Derivators in Higher Category Theory (A09)

这个项目的主要目标是在Grothendieck的导数理论中引入和发展新的观点，以便弥合与同伦理论的其他方法的差距，例如拟范畴。这些框架最近在代数K-理论的研究中有了显著的应用。通过考察Grothendieck理论的变体，我们旨在阐明更高范畴理论和K-理论之间的关系，以及出现在代数几何和等变同伦理论中的下降概念。

The primary goal of this project is to introduce and develop new perspectives in Grothendieck's theory of derivators in order to bridge the gap with the other approaches to the homotopy theory of homotopy theories such as quasi-categories. These frameworks have had notable recent applications to the study of algebraic K-theory. By examining variations on Grothendieck's theory we aim to shed light on the relationship between higher category theory and K-theory as well as notions of descent appearing in algebraic geometry and equivariant homotopy theory.