{-# OPTIONS --without-K #-} module agda.cctt where open import agda.fibration open import agda.prelude open import agda.postulates open import agda.exp-path ---------------------------------------------------------------------- -- The composition structure from "Cartesian Cubical Type Theory" -- by Angiuli et al ---------------------------------------------------------------------- CCTT : {l : Level} (P : ℘ (Set l)) → ------------- Set (ℓ₁ ⊔ l) CCTT P = (φ : Set) (_ : cof φ) (p : (i : 𝕀) → φ → P i) (i : 𝕀) (a : P i) (_ : p i ↗ a) → ----------------------------------------- Σ f ∶ (Π 𝕀 P) , (f i ≡ a) × ∀ j → p j ↗ f j