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typos
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martinescardo committed Sep 19, 2024
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Expand Up @@ -1331,14 +1331,14 @@ Markov's Principle. We leave this as an open problem.
Added 18th September 2024. There is another way of looking at the
above development, which gives rise to a further question.

We have the restriction map r : (ℕ → ℕ) → (ℕ → ℕ) defined by r f = f ∘ ι.
We have the restriction map r : (ℕ → ℕ) → (ℕ → ℕ) defined by r f = f ∘ ι.

For any map f : X → Y we have that

X ≃ Σ y ꞉ Y , Σ x ꞉ X , f x = y
= Σ y ꞉ Y , fiber f y.

With X = (ℕ → ℕ) and Y = (ℕ → ℕ) and f = r, the definition of
With X = (ℕ → ℕ) and Y = (ℕ → ℕ) and f = r, the definition of
_extends_, together with the fact that _∼_ coincides with _=_ under
function extensionality, the above specializes to

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