Delete equality module
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@ -5,9 +5,6 @@ module Cat.Categories.Cat where
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open import Cat.Prelude renaming (proj₁ to fst ; proj₂ to snd)
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open import Cubical
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open import Cubical.Sigma
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open import Cat.Category
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open import Cat.Category.Functor
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open import Cat.Category.Product
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@ -15,9 +12,6 @@ open import Cat.Category.Exponential hiding (_×_ ; product)
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open import Cat.Category.NaturalTransformation
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open import Cat.Categories.Fun
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open import Cat.Equality
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open Equality.Data.Product
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-- The category of categories
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module _ (ℓ ℓ' : Level) where
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private
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@ -1,21 +1,18 @@
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{-# OPTIONS --allow-unsolved-metas #-}
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module Cat.Categories.Cube where
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open import Cat.Prelude
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open import Level
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open import Data.Bool hiding (T)
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open import Data.Sum hiding ([_,_])
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open import Data.Unit
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open import Data.Empty
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open import Data.Product
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open import Cubical
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open import Function
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open import Relation.Nullary
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open import Relation.Nullary.Decidable
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open import Cat.Category
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open import Cat.Category.Functor
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open import Cat.Equality
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open Equality.Data.Product
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-- See chapter 1 for a discussion on how presheaf categories are CwF's.
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@ -1,17 +1,10 @@
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{-# OPTIONS --allow-unsolved-metas #-}
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module Cat.Categories.Fam where
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open import Agda.Primitive
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open import Data.Product
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open import Cat.Prelude
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import Function
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open import Cubical
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open import Cubical.Universe
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open import Cat.Category
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open import Cat.Equality
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open Equality.Data.Product
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module _ (ℓa ℓb : Level) where
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private
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@ -2,14 +2,10 @@
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module Cat.Category.Yoneda where
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open import Agda.Primitive
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open import Data.Product
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open import Cubical
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open import Cubical.NType.Properties
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open import Cat.Prelude
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open import Cat.Category
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open import Cat.Category.Functor
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open import Cat.Equality
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open import Cat.Categories.Fun
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open import Cat.Categories.Sets hiding (presheaf)
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@ -1,22 +0,0 @@
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{-# OPTIONS --cubical #-}
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-- Defines equality-principles for data-types from the standard library.
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module Cat.Equality where
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open import Level
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open import Cubical
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-- _[_≡_] = PathP
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module Equality where
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module Data where
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module Product where
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open import Data.Product
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module _ {ℓa ℓb : Level} {A : Set ℓa} {B : A → Set ℓb} {a b : Σ A B}
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(proj₁≡ : (λ _ → A) [ proj₁ a ≡ proj₁ b ])
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(proj₂≡ : (λ i → B (proj₁≡ i)) [ proj₂ a ≡ proj₂ b ]) where
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Σ≡ : a ≡ b
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proj₁ (Σ≡ i) = proj₁≡ i
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proj₂ (Σ≡ i) = proj₂≡ i
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@ -24,6 +24,8 @@ open import Cubical.NType.Properties
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( lemPropF ; lemSig ; lemSigP ; isSetIsProp
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; propPi ; propHasLevel ; setPi ; propSet)
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public
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open import Cubical.Sigma using (setSig) public
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open import Cubical.Universe using (hSet) public
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-----------------
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-- * Utilities --
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@ -38,3 +40,11 @@ open import Cubical.NType.Properties
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∃!-syntax = ∃
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syntax ∃!-syntax (λ x → B) = ∃![ x ] B
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module _ {ℓa ℓb : Level} {A : Set ℓa} {B : A → Set ℓb} {a b : Σ A B}
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(proj₁≡ : (λ _ → A) [ proj₁ a ≡ proj₁ b ])
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(proj₂≡ : (λ i → B (proj₁≡ i)) [ proj₂ a ≡ proj₂ b ]) where
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Σ≡ : a ≡ b
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proj₁ (Σ≡ i) = proj₁≡ i
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proj₂ (Σ≡ i) = proj₂≡ i
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