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Simplify qualified imports, change make-target: clean

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Frederik Hanghøj Iversen 2018-03-21 12:28:26 +01:00
parent e98ed89db5
commit 890154a81d
2 changed files with 10 additions and 8 deletions
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2
Makefile
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@ -2,4 +2,4 @@ build: src/**.agda
agda src/Cat.agda agda src/Cat.agda
clean: clean:
rm src/**/*.agdai find src -name "*.agdai" -type f -delete

16
src/Cat/Categories/Sets.agda
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@ -16,9 +16,11 @@ open import Cat.Category
open import Cat.Category.Functor open import Cat.Category.Functor
open import Cat.Category.Product open import Cat.Category.Product
open import Cat.Wishlist 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 _⊙_ : {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 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 module _ {ℓa ℓb : Level} {A : Set ℓa} {P : A → Set ℓb} where
lem2 : ((x : A) → isProp (P x)) → (p q : Σ A P) lem2 : ((x : A) → isProp (P x)) → (p q : Σ A P)
→ (p ≡ q) ≃ (proj₁ p ≡ proj₁ q) → (p ≡ q) ≃ (proj₁ p ≡ proj₁ q)
lem2 pA p q = Eeq.fromIsomorphism iso lem2 pA p q = fromIsomorphism iso
where where
f : p ≡ q → proj₁ p ≡ proj₁ q f : p ≡ q → proj₁ p ≡ proj₁ q
f e i = proj₁ (e i) f e i = proj₁ (e i)
@ -186,7 +188,7 @@ module _ (ℓ : Level) where
iso : Σ A P Eqv.≅ Σ A Q iso : Σ A P Eqv.≅ Σ A Q
iso = f , g , inv iso = f , g , inv
res : Σ A P ≃ Σ A Q 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 module _ {ℓa ℓb : Level} {A : Set ℓa} {B : Set ℓb} where
lem4 : isSet A → isSet B → (f : A → B) lem4 : isSet A → isSet B → (f : A → B)
@ -207,7 +209,7 @@ module _ (ℓ : Level) where
{ verso-recto = funExt re-ve { verso-recto = funExt re-ve
; recto-verso = funExt ve-re ; recto-verso = funExt ve-re
} }
in Eeq.fromIsomorphism iso in fromIsomorphism iso
module _ {hA hB : Object} where module _ {hA hB : Object} where
private private
@ -240,7 +242,7 @@ module _ (ℓ : Level) where
eqv : Σ (A → B) (isEquiv A B) Eqv.≅ (A ≃ B) eqv : Σ (A → B) (isEquiv A B) Eqv.≅ (A ≃ B)
eqv = obv , inv , areInv eqv = obv , inv , areInv
hh : Σ (A → B) (isEquiv A B) ≃ (A ≃ B) hh : Σ (A → B) (isEquiv A B) ≃ (A ≃ B)
hh = Eeq.fromIsomorphism eqv hh = fromIsomorphism eqv
-- lem2 with propIsSet -- lem2 with propIsSet
step2 : (A ≡ B) ≃ (hA ≡ hB) 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 -- Go from an isomorphism on sets to an isomorphism on homotopic sets
trivial? : (hA ≅ hB) ≃ Σ (A → B) isIso trivial? : (hA ≅ hB) ≃ Σ (A → B) isIso
trivial? = sym≃ (Eeq.fromIsomorphism res) trivial? = sym≃ (fromIsomorphism res)
where where
fwd : Σ (A → B) isIso → hA ≅ hB fwd : Σ (A → B) isIso → hA ≅ hB
fwd (f , g , inv) = f , g , inv.toPair fwd (f , g , inv) = f , g , inv.toPair