47 lines
852 B
Agda
47 lines
852 B
Agda
{-# OPTIONS --cubical --allow-unsolved-metas #-}
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module Cat.Category.Bij where
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open import Cubical hiding ( Id )
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open import Cubical.FromStdLib
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module _ {A : Set} {a : A} {P : A → Set} where
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Q : A → Set
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Q a = A
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t : Σ[ a ∈ A ] P a → Q a
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t (a , Pa) = a
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u : Q a → Σ[ a ∈ A ] P a
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u a = a , {!!}
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tu-bij : (a : Q a) → (t ∘ u) a ≡ a
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tu-bij a = refl
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v : P a → Q a
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v x = {!!}
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w : Q a → P a
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w x = {!!}
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vw-bij : (a : P a) → (w ∘ v) a ≡ a
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vw-bij a = {!!}
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-- tubij a with (t ∘ u) a
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-- ... | q = {!!}
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data Id {A : Set} (a : A) : Set where
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id : A → Id a
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data Id' {A : Set} (a : A) : Set where
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id' : A → Id' a
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T U : Set
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T = Id a
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U = Id' a
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f : T → U
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f (id x) = id' x
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g : U → T
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g (id' x) = id x
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fg-bij : (x : U) → (f ∘ g) x ≡ x
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fg-bij (id' x) = {!!}
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