Update CHANGELOG and remove --allow-unsolved-metas pragma
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BACKLOG.md
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BACKLOG.md
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Backlog
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=======
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Prove postulates in `Cat.Wishlist`:
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* `ntypeCommulative : n ≤ m → HasLevel ⟨ n ⟩₋₂ A → HasLevel ⟨ m ⟩₋₂ A`
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Prove that these two formulations of univalence are equivalent:
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∀ A B → isEquiv (A ≡ B) (A ≅ B) (idToIso A B)
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∀ A → isContr (Σ[ X ∈ Object ] A ≅ X)
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Prove univalence for the category of
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* functors and natural transformations
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Prove:
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* `isProp (Product ...)`
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* `isProp (HasProducts ...)`
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In AreInverses, dont use the "point-free" version. I.e.:
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Rename composition in categories
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In stead of using AreInverses, just use a sigma-type
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`∀ x → f x ≡ g x` rather than `f ≡ g`
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Ideas for future work
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---------------------
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26
CHANGELOG.md
26
CHANGELOG.md
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Change log
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=========
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Version 1.5.0
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-------------
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Prove postulates in `Cat.Wishlist`:
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* `ntypeCommulative : n ≤ m → HasLevel ⟨ n ⟩₋₂ A → HasLevel ⟨ m ⟩₋₂ A`
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Prove that these two formulations of univalence are equivalent:
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∀ A B → isEquiv (A ≡ B) (A ≅ B) (id-to-iso A B)
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∀ A → isContr (Σ[ X ∈ Object ] A ≅ X)
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Prove univalence for the category of...
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* the opposite category
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* sets
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* "pair" category
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Finish the proof that products are propositional:
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* `isProp (Product ...)`
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* `isProp (HasProducts ...)`
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Remove --allow-unsolved-metas pragma from various files
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Also renamed a lot of different projections. E.g. arrow-composition, etc..
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Version 1.4.1
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-------------
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Defines a module to work with equivalence providing a way to go between
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-- | The category of homotopy sets
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{-# OPTIONS --allow-unsolved-metas --cubical --caching #-}
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{-# OPTIONS --cubical --caching #-}
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module Cat.Categories.Sets where
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open import Cat.Prelude as P
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-- ------
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--
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-- Propositionality for all laws about the category.
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{-# OPTIONS --allow-unsolved-metas --cubical #-}
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{-# OPTIONS --cubical #-}
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module Cat.Category where
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@ -17,7 +17,7 @@ These two formulations are proven to be equivalent:
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The monoidal representation is exposed by default from this module.
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---}
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{-# OPTIONS --cubical --allow-unsolved-metas #-}
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{-# OPTIONS --cubical #-}
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module Cat.Category.Monad where
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open import Cat.Prelude
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{---
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The Kleisli formulation of monads
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---}
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{-# OPTIONS --cubical --allow-unsolved-metas #-}
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{-# OPTIONS --cubical #-}
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open import Agda.Primitive
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open import Cat.Prelude
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{---
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Monoidal formulation of monads
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---}
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{-# OPTIONS --cubical --allow-unsolved-metas #-}
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{-# OPTIONS --cubical #-}
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open import Agda.Primitive
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open import Cat.Prelude
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{-
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This module provides construction 2.3 in [voe]
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-}
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{-# OPTIONS --cubical --allow-unsolved-metas --caching #-}
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{-# OPTIONS --cubical --caching #-}
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module Cat.Category.Monad.Voevodsky where
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open import Cat.Prelude
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-- Functions for manipulating the above:
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--
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-- * A composition operator.
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{-# OPTIONS --allow-unsolved-metas --cubical #-}
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{-# OPTIONS --cubical #-}
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open import Cat.Prelude
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open import Data.Nat using (_≤′_ ; ≤′-refl ; ≤′-step)
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{-# OPTIONS --allow-unsolved-metas --cubical --caching #-}
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{-# OPTIONS --cubical --caching #-}
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module Cat.Category.Product where
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open import Cat.Prelude as P hiding (_×_ ; fst ; snd)
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@ -299,7 +299,7 @@ module Try0 {ℓa ℓb : Level} {ℂ : Category ℓa ℓb}
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open Σ ump renaming (fst to f')
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open Σ (snd ump) renaming (fst to f'-cond)
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𝒻 : Arrow 𝒴 𝒳
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𝒻 = f' , {!f'-cond!}
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𝒻 = f' , f'-cond
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contractible : (f : Arrow 𝒴 𝒳) → 𝒻 ≡ f
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contractible ff@(f , f-cond) = res
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where
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{-# OPTIONS --allow-unsolved-metas --cubical #-}
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{-# OPTIONS --cubical #-}
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module Cat.Category.Yoneda where
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{-# OPTIONS --allow-unsolved-metas --cubical #-}
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{-# OPTIONS --cubical #-}
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module Cat.Equivalence where
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open import Cubical.Primitives
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