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src/VanDoornDissertation/PropTrunc.agda
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src/VanDoornDissertation/PropTrunc.agda
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{-# OPTIONS --cubical #-}
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module VanDoornDissertation.PropTrunc where
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open import Cubical.Foundations.Prelude
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open import Cubical.Foundations.Equiv
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open import Cubical.HITs.Truncation
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open import Cubical.HITs.PropositionalTruncation
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-- Theorem 3.1.8. The map A 7 → {A}∞ satisfies all the properties of the propositional
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-- truncation ‖−‖, including the universe level and judgmental computation rule on point
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-- constructors.
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ptrunc-equiv-trunc : {A : Type} → ∥ A ∥₁ ≃ (∥ A ∥ 1)
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ptrunc-equiv-trunc {A} = f , record { equiv-proof = eqv } where
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f : ∥ A ∥₁ → (∥ A ∥ 1)
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f ∣ x ∣₁ = ∣ x ∣
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f (squash₁ x y i) = {! !}
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g : ∥ A ∥ 1 → ∥ A ∥₁
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g ∣ x ∣ = ∣ x ∣₁
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g (hub f₁) = {! !}
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g (spoke f₁ x i) = {! !}
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eqv : (y : ∥ A ∥ 1) → isContr (fiber f y)
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eqv y = {! !} , {! !}
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{-# OPTIONS --cubical #-}
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module VanDoornDissertation.Spectral.Algebra.SpectralSequence where
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open import Cubical.Foundations.Prelude
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record convergent-spectral-sequence : Type where
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