Higher-Dimensional Categories

Higher-dimensional categories are mathematical frameworks that extend the concept of categories, which organize objects and the relationships (morphisms) between them. In higher categories, not only are the arrows between objects considered, but also transformations between those arrows, and further levels of relationships between those transformations, creating multiple layers of connections. This layered structure captures complex systems where interactions occur at various levels, enabling a more nuanced understanding of mathematical and logical structures, often used in advanced fields like topology, algebra, and computer science.