Higher-Dimensional Category

Higher-dimensional categories are mathematical structures that extend the concept of categories, which consist of objects and arrows (morphisms) between them. In higher-dimensional categories, these arrows themselves can have arrows between them, called 2-morphisms, and this idea can continue to even higher levels. This allows for a more nuanced and flexible way to describe complex relationships and transformations in mathematics, computer science, and physics. Think of it as a framework that captures not just simple connections, but also the ways those connections can relate and transform, across multiple layers of interaction.