Higher category theory

Higher category theory is a branch of mathematics that studies collections of objects and the relationships between them, extending traditional categories to include relationships between relationships, and so on, in multiple levels. Imagine not just points and arrows between points, but arrows between arrows, and even higher levels of connections. This framework helps mathematicians understand complex structures in areas like topology, algebra, and computer science by capturing nuanced patterns and symmetries that can't be described with simple hierarchical models. Essentially, it’s an advanced language for describing interconnected systems with layered, multi-dimensional relationships.