SCT.VolumeI.Chapter02.Section03.RezkAxiom

Complete compiler-highlighted source. Follow a symbol to its declaration.

# The Rezk axiom

`axiom:C_Rezk_Axiom` asserts that the identity-isomorphism functor
constructed in the preceding module is an equivalence. Its codomain is
the specified iterated pullback, not a new primitive category.

```agda
{-# OPTIONS --safe --without-K #-}
open import Agda.Primitive using (Level; _⊔_)
open import SCT.VolumeI.Chapter01.Theory using (Theory)
import SCT.VolumeI.Chapter01.Section04.MappingAnimae as Mapping
import SCT.VolumeI.Chapter01.Section07.FunctorCategories as Categories
import SCT.VolumeI.Chapter01.Section06.PullbackLaws as Laws
import SCT.VolumeI.Chapter02.Section01.WalkingMorphism as Walking
import SCT.VolumeI.Chapter02.Section01.IntervalEndpoints as Endpoints

module SCT.VolumeI.Chapter02.Section03.RezkAxiom
  {c m a : Level} (𝒯 : Theory c m a) (M : Mapping.MappingAnimae 𝒯)
  (ℱ : Categories.FunctorCategories 𝒯 M) (P : Laws.PullbackStructure 𝒯)
  (I : Walking.WalkingMorphism 𝒯) (E : Endpoints.IntervalEndpoints 𝒯 M ℱ P I) where

open import SCT.VolumeI.Chapter02.Section03.IdentityIsomorphisms 𝒯 M ℱ P I E public

record RezkAxiom : Set (c ⊔ m) where
  field
    rezk-isEquiv : (C : CAT) → IsEquiv (identityIso {C})
```