Univalence is a concept in mathematics, particularly in the field of homotopy theory. It refers to a property of certain types of mathematical structures, where a function or a map is considered "univalent" if it is injective, meaning it assigns distinct outputs to distinct inputs. This property is important for understanding how different spaces can be related to each other. In the context of type theory, univalence is a principle introduced by Vladimir Voevodsky. It states that equivalent mathematical structures can be treated as identical. This idea has significant implications for the foundations of mathematics, allowing for a more flexible approach to reasoning about mathematical objects and their relationships.