Homotopy type theory isn’t magic, but it nicely explores the difference between (strict) equality and context dependent equivalence. (Okay, technically that’s u

Homotopy type theory isn’t magic, but it nicely explores the difference between (strict) equality and context dependent equivalence. (Okay, technically that’s univalence.) I think HoTT nicely capstones the idea algebra and geometry are equivalent by pointing out that semantics itself is defined by the topology of categorical diagrams — and anywhere we find compatible topology is equivalent. Neat.