Export TypeIsomorphism as an alias for Equivalence.Isomorphism

This commit is contained in:
Frederik Hanghøj Iversen 2018-04-09 18:10:39 +02:00
parent 8c6e327b1c
commit fd18985e53
4 changed files with 15 additions and 8 deletions

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@ -29,7 +29,11 @@
module Cat.Category where
open import Cat.Prelude
open import Cat.Equivalence as Equivalence renaming (_≅_ to _≈_ ; Isomorphism to TypeIsomorphism) hiding (preorder≅)
import Cat.Equivalence
open Cat.Equivalence public using () renaming (Isomorphism to TypeIsomorphism)
open Cat.Equivalence
renaming (_≅_ to _≈_)
hiding (preorder≅ ; Isomorphism)
import Function
@ -485,7 +489,7 @@ module Opposite {a b : Level} where
open IsPreCategory isPreCategory
module _ {A B : .Object} where
k : Equivalence.Isomorphism (.idToIso A B)
k : TypeIsomorphism (.idToIso A B)
k = toIso _ _ .univalent
open Σ k renaming (fst to η ; snd to inv-η)
open AreInverses inv-η
@ -537,7 +541,7 @@ module Opposite {a b : Level} where
x )
}
h : Equivalence.Isomorphism (idToIso A B)
h : TypeIsomorphism (idToIso A B)
h = ζ , inv-ζ
isCategory : IsCategory opRaw

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@ -209,3 +209,6 @@ module _ {a b : Level} ( : Category a b) where
Monoidal≃Kleisli : M.Monad K.Monad
Monoidal≃Kleisli = forth , eqv
Monoidal≡Kleisli : M.Monad K.Monad
Monoidal≡Kleisli = ua (forth , eqv)

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@ -172,9 +172,6 @@ module voe {a b : Level} ( : Category a b) where
where
t' : ((Monoidal→Kleisli Kleisli→Monoidal) §2-3.§2.toMonad {omap} {pure})
§2-3.§2.toMonad
cong-d : {} {A : Set } {'} {B : A Set '} {x y : A}
(f : (x : A) B x) (eq : x y) PathP (\ i B (eq i)) (f x) (f y)
cong-d f p = λ i f (p i)
t' = cong (\ φ φ §2-3.§2.toMonad) re-ve
t : (§2-fromMonad (Monoidal→Kleisli Kleisli→Monoidal) §2-3.§2.toMonad {omap} {pure})
(§2-fromMonad §2-3.§2.toMonad)

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@ -203,12 +203,15 @@ module Try0 {a b : Level} { : Category a b}
: ((X , xa , xb) (Y , ya , yb))
(Σ[ p (X Y) ] (PathP (λ i .Arrow (p i) A) xa ya) × (PathP (λ i .Arrow (p i) B) xb yb))
step0
= (λ p (λ i fst (p i)) , (λ i fst (snd (p i))) , (λ i snd (snd (p i))))
, (λ x λ i fst x i , (fst (snd x) i) , (snd (snd x) i))
= (λ p cong fst p , cong-d (fst snd) p , cong-d (snd snd) p)
-- , (λ x → λ i → fst x i , (fst (snd x) i) , (snd (snd x) i))
, (λ{ (p , q , r) Σ≡ p λ i q i , r i})
, record
{ verso-recto = {!!}
; recto-verso = {!!}
}
where
open import Function renaming (_∘_ to _⊙_)
step1
: (Σ[ p (X Y) ] (PathP (λ i .Arrow (p i) A) xa ya) × (PathP (λ i .Arrow (p i) B) xb yb))
Σ (X .≅ Y) (λ iso