Voevodsky's Univalence Axiom

Voevodsky's Univalence Axiom, central to Homotopy Type Theory, states that equivalent mathematical structures can be considered identical. In essence, if two constructions are "equivalent"—meaning they behave the same in every relevant way—they can be treated as equal within the system. This principle blurs the line between sameness and equivalence, allowing mathematicians to work more flexibly and intuitively with structures like shapes or spaces. It formalizes the idea that the essence of a structure is captured by its properties and relationships, fostering a unified perspective in the foundations of mathematics.