Categorification is a mathematical process that transforms set-theoretic concepts into higher-dimensional structures called categories. In this context, objects and morphisms (arrows) in a category can represent more complex relationships than mere sets, allowing mathematicians to explore deeper connections between different areas of mathematics. This approach often involves replacing elements of a set with objects in a category, leading to a richer framework for understanding mathematical phenomena. For example, the concept of a number can be categorified into a category of objects that represent that number, such as vector spaces of dimension corresponding to the number, along with linear transformations between them.