Higher-Dimensional Type Theory

Higher-Dimensional Type Theory is an advanced mathematical framework that extends traditional type systems to describe not only objects and their relationships but also relationships between those relationships, and so on, across multiple levels. It provides tools to analyze complex structures with multiple layers of connections, allowing mathematicians and computer scientists to reason about intricate systems—such as flexible programs or interconnected data—more precisely. By capturing these multi-layered interactions, higher-dimensional type theory offers a powerful language for formalizing and verifying complex, layered processes in a rigorous way.