Rely on global cubical again

This commit is contained in:
Frederik Hanghøj Iversen 2018-02-16 11:36:44 +01:00
parent 8a3a519955
commit 23c458983c
6 changed files with 51 additions and 51 deletions

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@ -2,13 +2,11 @@ name: cat
-- version: 0.0.1 -- version: 0.0.1
-- description: -- description:
-- A formalization of category theory in Agda using cubical type theory. -- A formalization of category theory in Agda using cubical type theory.
-- depend: depend:
-- standard-library standard-library
-- cubical cubical
include: include:
src src
libs/agda-stdlib/src
libs/cubical/src
-- libraries: -- libraries:
-- libs/agda-stdlib -- libs/agda-stdlib
-- libs/cubical -- libs/cubical

@ -1 +1 @@
Subproject commit b5bfbc3c170b0bd0c9aaac1b4d4b3f9b06832bf6 Subproject commit 157497a5335ad0069c7aaffbc65932c40a28ee68

@ -1 +1 @@
Subproject commit 1d6730c4999daa2b04e9dd39faa0791d0b5c3b48 Subproject commit 12c2c628e9e202f1698a4c32e0356d5ca8cb6151

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@ -7,6 +7,7 @@ open import Function
open import Data.Product open import Data.Product
import Cubical.GradLemma import Cubical.GradLemma
module UIP = Cubical.GradLemma module UIP = Cubical.GradLemma
open import Cubical.Sigma
open import Cat.Category open import Cat.Category
open import Cat.Category.Functor open import Cat.Category.Functor
@ -118,48 +119,49 @@ module _ {c c' d d' : Level} { : Category c c'} {𝔻 : Cat
lem : (λ _ Natural F G θ) [ (λ f θNat f) (λ f θNat' f) ] lem : (λ _ Natural F G θ) [ (λ f θNat f) (λ f θNat' f) ]
lem = λ i f 𝔻.arrowIsSet _ _ (θNat f) (θNat' f) i lem = λ i f 𝔻.arrowIsSet _ _ (θNat f) (θNat' f) i
naturalTransformationIsSets f : isSet (NaturalTransformation F G) naturalTransformationIsSets : isSet (NaturalTransformation F G)
f a b p q i = res naturalTransformationIsSets = {!sigPresSet!}
where -- f a b p q i = res
k : (θ : Transformation F G) (xx yy : Natural F G θ) xx yy
k θ x y = let kk = naturalIsProp θ x y in {!!}
res : a b
res j = {!!} , {!!}
-- naturalTransformationIsSets σa σb p q
-- where -- where
-- -- In Andrea's proof `lemSig` he proves something very similiar to -- k : (θ : Transformation F G) → (xx yy : Natural F G θ) → xx ≡ yy
-- -- what I'm doing here, just for `Cubical.FromPathPrelude.Σ` rather -- k θ x y = let kk = naturalIsProp θ x y in {!!}
-- -- than `Σ`. In that proof, he just needs *one* proof that the first -- res : a ≡ b
-- -- components are equal - hence the arbitrary usage of `p` here. -- res j = {!!} , {!!}
-- secretSauce : proj₁ σa ≡ proj₁ σb -- -- naturalTransformationIsSets σa σb p q
-- secretSauce i = proj₁ (p i) -- -- where
-- lemSig : σa ≡ σb -- -- -- In Andrea's proof `lemSig` he proves something very similiar to
-- lemSig i = (secretSauce i) , (UIP.lemPropF naturalIsProp secretSauce) {proj₂ σa} {proj₂ σb} i -- -- -- what I'm doing here, just for `Cubical.FromPathPrelude.Σ` rather
-- res : p ≡ q -- -- -- than `Σ`. In that proof, he just needs *one* proof that the first
-- res = {!!} -- -- -- components are equal - hence the arbitrary usage of `p` here.
naturalTransformationIsSets (θ , θNat) (η , ηNat) p q i j -- -- secretSauce : proj₁ σa ≡ proj₁ σb
= θ-η -- -- secretSauce i = proj₁ (p i)
-- `i or `j - `p'` or `q'`? -- -- lemSig : σa ≡ σb
, {!!} -- UIP.lemPropF {B = Natural F G} (λ x → {!!}) {(θ , θNat)} {(η , ηNat)} {!!} i -- -- lemSig i = (secretSauce i) , (UIP.lemPropF naturalIsProp secretSauce) {proj₂ σa} {proj₂ σb} i
-- naturalIsSet i (λ i → {!!} i) {!!} {!!} i j -- -- res : p ≡ q
-- naturalIsSet {!p''!} {!p''!} {!!} i j -- -- res = {!!}
-- λ f k → 𝔻.arrowIsSet (λ l → proj₂ (p l) f k) (λ l → proj₂ (p l) f k) {!!} {!!} -- naturalTransformationIsSets (θ , θNat) (η , ηNat) p q i j
where -- = θ-η
θ≡η θ≡η' : θ η -- -- `i or `j - `p'` or `q'`?
θ≡η i = proj₁ (p i) -- , {!!} -- UIP.lemPropF {B = Natural F G} (λ x → {!!}) {(θ , θNat)} {(η , ηNat)} {!!} i
θ≡η' i = proj₁ (q i) -- -- naturalIsSet i (λ i → {!!} i) {!!} {!!} i j
θ-η : Transformation F G -- -- naturalIsSet {!p''!} {!p''!} {!!} i j
θ-η = transformationIsSet _ _ θ≡η θ≡η' i j -- -- λ f k → 𝔻.arrowIsSet (λ l → proj₂ (p l) f k) (λ l → proj₂ (p l) f k) {!!} {!!}
θNat≡ηNat : (λ i Natural F G (θ≡η i)) [ θNat ηNat ] -- where
θNat≡ηNat i = proj₂ (p i) -- θ≡η θ≡η' : θ ≡ η
θNat≡ηNat' : (λ i Natural F G (θ≡η' i)) [ θNat ηNat ] -- θ≡η i = proj₁ (p i)
θNat≡ηNat' i = proj₂ (q i) -- θ≡η' i = proj₁ (q i)
k : Natural F G (θ≡η i) -- θ-η : Transformation F G
k = θNat≡ηNat i -- θ-η = transformationIsSet _ _ θ≡η θ≡η' i j
k' : Natural F G (θ≡η' i) -- θNat≡ηNat : (λ i → Natural F G (θ≡η i)) [ θNat ≡ ηNat ]
k' = θNat≡ηNat' i -- θNat≡ηNat i = proj₂ (p i)
t : Natural F G θ-η -- θNat≡ηNat' : (λ i → Natural F G (θ≡η' i)) [ θNat ≡ ηNat ]
t = naturalIsProp {!θ!} {!!} {!!} {!!} -- θNat≡ηNat' i = proj₂ (q i)
-- k : Natural F G (θ≡η i)
-- k = θNat≡ηNat i
-- k' : Natural F G (θ≡η' i)
-- k' = θNat≡ηNat' i
-- t : Natural F G θ-η
-- t = naturalIsProp {!θ!} {!!} {!!} {!!}
module _ {A B C D : Functor 𝔻} {θ' : NaturalTransformation A B} module _ {A B C D : Functor 𝔻} {θ' : NaturalTransformation A B}
{η' : NaturalTransformation B C} {ζ' : NaturalTransformation C D} where {η' : NaturalTransformation B C} {ζ' : NaturalTransformation C D} where

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@ -12,7 +12,7 @@ open import Data.Product renaming
open import Data.Empty open import Data.Empty
import Function import Function
open import Cubical open import Cubical
open import Cubical.GradLemma using ( propIsEquiv ) open import Cubical.NType.Properties using ( propIsEquiv )
∃! : {a b} {A : Set a} ∃! : {a b} {A : Set a}
(A Set b) Set (a b) (A Set b) Set (a b)

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@ -83,7 +83,7 @@ module _
IsFunctorIsProp' isF0 isF1 = lemPropF {B = IsFunctor 𝔻} IsFunctorIsProp' isF0 isF1 = lemPropF {B = IsFunctor 𝔻}
(\ F IsFunctorIsProp {F = F}) (\ i F i) (\ F IsFunctorIsProp {F = F}) (\ i F i)
where where
open import Cubical.GradLemma using (lemPropF) open import Cubical.NType.Properties using (lemPropF)
module _ { ' : Level} { 𝔻 : Category '} where module _ { ' : Level} { 𝔻 : Category '} where
Functor≡ : {F G : Functor 𝔻} Functor≡ : {F G : Functor 𝔻}