rezk-types

Rezk types encode local univalence, collapsing isomorphisms to identities within complete Segal spaces. This bridge between higher category theory and type theory lets you treat structurally equivalent objects as definitionally equal, eliminating manual conversion steps.

Segal types are higher-categorical structures where composition is weakly associative and unital. Use them when formalizing ∞-categories in type theory, particularly to model spaces where morphism composition reflects real compositional semantics rather than strict equations.

Define Segal types using Lean4 semantics, assert local univalence, then construct is-iso, Iso, and id-to-iso proofs. InfinityCosmos provides the synthetic ∞-category framework; integrate Rezk completion to formalize equivalences as identities.

The quick start guides you through defining a simple Segal type and observing isomorphisms collapse to identities. Core concepts—local univalence and type equivalence—are learnable incrementally, though comfort with higher-categorical intuition accelerates adoption.

Rezk types specifically target complete Segal spaces, encoding univalence locally within a type rather than globally. This scope lets you reason about isomorphisms as equalities in controlled contexts without requiring full univalent type theory.