Homotopy Type Theory
Homotopy Type Theory (HoTT) is a branch of mathematical logic that combines concepts from homotopy theory and type theory. It provides a framework for understanding mathematical structures through types, which can represent both objects and their relationships. In HoTT, types can be seen as spaces, and paths between points in these spaces correspond to proofs of equality between objects.
One of the key features of HoTT is the notion of equivalence, which allows for a flexible understanding of when two types can be considered the same. This approach has implications for category theory and formal verification, making it a valuable tool in both mathematics and computer science.