diff --git a/src/HottBook/Chapter2.lagda.md b/src/HottBook/Chapter2.lagda.md new file mode 100644 index 0000000..b2dec1a --- /dev/null +++ b/src/HottBook/Chapter2.lagda.md @@ -0,0 +1,4 @@ +``` +module HottBook.Chapter2 where +``` + diff --git a/src/HottBook/Chapter2Exercises.lagda.md b/src/HottBook/Chapter2Exercises.lagda.md new file mode 100644 index 0000000..dc7b82f --- /dev/null +++ b/src/HottBook/Chapter2Exercises.lagda.md @@ -0,0 +1,43 @@ +``` +module HottBook.Chapter2Exercises where + +open import Relation.Binary.PropositionalEquality +Type = Set +transport = subst +``` + +## Exercise 2.4 + +Define, by induction on n, a general notion of n-dimensional path in a type A, +simultaneously with the type of boundaries for such paths. + +(tracked in [#6][6]) + +[6]: https://git.mzhang.io/school/cubical/issues/6 + +``` + +``` + +## Exercise 2.5 + +Prove that the functions [2.3.6] and (2.3.7) are inverse equivalences. + +[2.3.6]: https://hott.github.io/book/hott-ebook-1357-gbe0b8e2.pdf#equation.2.3.6 +[2.3.7]: https://hott.github.io/book/hott-ebook-1357-gbe0b8e2.pdf#equation.2.3.7 + +Here is the definition of transportconst from lemma 2.3.5: + +``` +transportconst : {A : Type} {x y : A} (B : Type) → (p : x ≡ y) → (b : B) + → transport (λ _ → B) p b ≡ b +transportconst {A} {x} B p b = + let + D : (x y : A) → (p : x ≡ y) → Type + D x y p = transport (λ _ → B) p b ≡ b + + d : (x : A) → D x x refl + d x = refl + in + J (λ x p → transport (λ _ → B) p b ≡ b) p (d x) +```