diff --git a/Makefile b/Makefile index f2e26be..1a3e6e8 100644 --- a/Makefile +++ b/Makefile @@ -2,4 +2,4 @@ build: src/**.agda agda src/Cat.agda clean: - rm src/**/*.agdai + find src -name "*.agdai" -type f -delete diff --git a/src/Cat/Categories/Sets.agda b/src/Cat/Categories/Sets.agda index ce94104..f109b0c 100644 --- a/src/Cat/Categories/Sets.agda +++ b/src/Cat/Categories/Sets.agda @@ -16,9 +16,11 @@ open import Cat.Category open import Cat.Category.Functor open import Cat.Category.Product open import Cat.Wishlist -open import Cat.Equivalence as Eqv renaming (module NoEta to Eeq) using (AreInverses ; module Equiv≃) +open import Cat.Equivalence as Eqv using (AreInverses ; module Equiv≃ ; module NoEta) -module Equivalence = Eeq.Equivalence′ +open NoEta + +module Equivalence = Equivalence′ _⊙_ : {ℓa ℓb ℓc : Level} {A : Set ℓa} {B : Set ℓb} {C : Set ℓc} → (A ≃ B) → (B ≃ C) → A ≃ C eqA ⊙ eqB = Equivalence.compose eqA eqB @@ -122,7 +124,7 @@ module _ (ℓ : Level) where module _ {ℓa ℓb : Level} {A : Set ℓa} {P : A → Set ℓb} where lem2 : ((x : A) → isProp (P x)) → (p q : Σ A P) → (p ≡ q) ≃ (proj₁ p ≡ proj₁ q) - lem2 pA p q = Eeq.fromIsomorphism iso + lem2 pA p q = fromIsomorphism iso where f : p ≡ q → proj₁ p ≡ proj₁ q f e i = proj₁ (e i) @@ -186,7 +188,7 @@ module _ (ℓ : Level) where iso : Σ A P Eqv.≅ Σ A Q iso = f , g , inv res : Σ A P ≃ Σ A Q - res = Eeq.fromIsomorphism iso + res = fromIsomorphism iso module _ {ℓa ℓb : Level} {A : Set ℓa} {B : Set ℓb} where lem4 : isSet A → isSet B → (f : A → B) @@ -207,7 +209,7 @@ module _ (ℓ : Level) where { verso-recto = funExt re-ve ; recto-verso = funExt ve-re } - in Eeq.fromIsomorphism iso + in fromIsomorphism iso module _ {hA hB : Object} where private @@ -240,7 +242,7 @@ module _ (ℓ : Level) where eqv : Σ (A → B) (isEquiv A B) Eqv.≅ (A ≃ B) eqv = obv , inv , areInv hh : Σ (A → B) (isEquiv A B) ≃ (A ≃ B) - hh = Eeq.fromIsomorphism eqv + hh = fromIsomorphism eqv -- lem2 with propIsSet step2 : (A ≡ B) ≃ (hA ≡ hB) @@ -248,7 +250,7 @@ module _ (ℓ : Level) where -- Go from an isomorphism on sets to an isomorphism on homotopic sets trivial? : (hA ≅ hB) ≃ Σ (A → B) isIso - trivial? = sym≃ (Eeq.fromIsomorphism res) + trivial? = sym≃ (fromIsomorphism res) where fwd : Σ (A → B) isIso → hA ≅ hB fwd (f , g , inv) = f , g , inv.toPair