diff --git a/html/book.toml b/html/book.toml index 8920053..e9c0af1 100644 --- a/html/book.toml +++ b/html/book.toml @@ -8,8 +8,8 @@ title = "Research" [preprocessor.katex] macros = "./macros.txt" -[preprocessor.graph] -command = "bun aux/preprocessGraph.ts" +# [preprocessor.graph] +# command = "bun aux/preprocessGraph.ts" [preprocessor.chapter-zero] levels = [0] diff --git a/html/src/front.md b/html/src/front.md index 438be5d..47f8cde 100644 --- a/html/src/front.md +++ b/html/src/front.md @@ -22,5 +22,6 @@ I have scaled down some of these materials to eBook size, for easier reading on [[ebook-sized pdf](https://git.mzhang.io/school/type-theory/src/branch/master/resources/MayConcise/ConciseRevised.pdf)] [[original pdf](https://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf)] - + Cubical Type Theory: a constructive interpretation of the univalence axiom (CCHM) (2015) [[ebook-sized pdf](https://git.mzhang.io/school/type-theory/raw/branch/master/resources/CCHM/main.pdf)] [[original pdf](https://arxiv.org/pdf/1611.02108)] diff --git a/src/CubicalHott/Chapter2.lagda.md b/src/CubicalHott/Chapter2.lagda.md index 5d11425..1ecb81b 100644 --- a/src/CubicalHott/Chapter2.lagda.md +++ b/src/CubicalHott/Chapter2.lagda.md @@ -201,20 +201,14 @@ module lemma2∙4∙12 where ``` module axiom2∙10∙3 where - Glue : ∀ {l l2} (A : Type l) - → {φ : I} - → (Te : Partial φ (Σ (Type l2) (λ T → T ≃ A))) - → Type l2 + -- Glue : ∀ {l l2} (A : Type l) + -- → {φ : I} + -- → (Te : Partial φ (Σ (Type l2) (λ T → T ≃ A))) + -- → Type l2 - id-equiv : isequiv id - - ua : ∀ {l} {A B : Type l} → A ≃ B → A ≡ B - ua {A = A} {B} eqv i = Glue B λ - { (i = i0) → A , eqv - ; (i = i1) → B , _ , id-equiv - } - -- postulate - -- ua : {l : Level} {A B : Type l} → (A ≃ B) → (A ≡ B) + postulate + -- TODO: Provide the definition for this after reading CCHM + ua : {l : Level} {A B : Type l} → (A ≃ B) → (A ≡ B) -- forward : {l : Level} {A B : Type l} → (eqv : A ≃ B) → (idtoeqv ∘ ua) eqv ≡ eqv -- -- forward eqv = {! !} @@ -225,7 +219,7 @@ module axiom2∙10∙3 where -- ua-eqv : {l : Level} {A : Type l} {B : Type l} → (A ≃ B) ≃ (A ≡ B) -- ua-eqv = ua , qinv-to-isequiv (mkQinv idtoeqv backward forward) -open axiom2∙10∙3 hiding (forward; backward) +open axiom2∙10∙3 ``` ### Remark 2.12.6 diff --git a/src/HottBook/Chapter7.lagda.md b/src/HottBook/Chapter7.lagda.md deleted file mode 100644 index 56b653e..0000000 --- a/src/HottBook/Chapter7.lagda.md +++ /dev/null @@ -1,18 +0,0 @@ -``` -module HottBook.Chapter7 where - -open import Agda.Primitive -open import HottBook.Chapter1 -open import HottBook.Chapter2 -open import HottBook.Chapter6 -``` - -## 7.1 Definition of $n$-types - -### Definition 7.1.1 - -``` -is-_-type : ℕ → Set → Set -is- zero -type X = 𝟙 -is- suc n -type X = (x y : X) → is- n -type (x ≡ y) -``` \ No newline at end of file diff --git a/src/HottBook/Chapter9.lagda.md b/src/HottBook/Chapter9.lagda.md deleted file mode 100644 index 5968ed2..0000000 --- a/src/HottBook/Chapter9.lagda.md +++ /dev/null @@ -1,38 +0,0 @@ -``` -module HottBook.Chapter9 where - -open import Agda.Primitive -open import HottBook.Chapter1 -``` - -## 9.1 Categories and precategories - -``` -record precat {l : Level} (A : Set l) : Set (lsuc l) where - field - hom : (a b : A) → Set - id' : (a : A) → hom a a - comp : {a b c : A} → hom a b → hom b c → hom a c - lol : (a b : A) → (f : hom a b) → (f ≡ comp f (id' b)) × (f ≡ comp (id' a) f) - -``` - -### Definition 9.1.2 - -``` --- record isIso {l : Level} {A : Set l} {PC : precat A} {a b : A} (f : precat.hom PC a b) : Set (lsuc l) where --- field --- g : precat.hom PC b a --- g-f : precat.comp f g ≡ precat.id' a -``` - -### Lemma 9.1.4 - -``` -idtoiso : {A : Set} - → (PC : precat A) - → (a b : A) - → a ≡ b - → precat.hom PC a b -idtoiso {A} PC a b refl = precat.id' PC a -``` \ No newline at end of file