The Axiom of Univalence
Read OriginalThis technical article delves into advanced type theory, examining identity types and the limitations of the uniqueness of identity proofs (UIP/axiom K). It discusses comparing types for equality, proposing isomorphism and then the more nuanced concept of equivalence inspired by homotopy theory. The article builds towards explaining Vladimir Voevodsky's Axiom of Univalence, which posits that equivalence between types can define their equality.
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