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zV2RB=JYTfL);XT!d&zCH5uCwQd$$ZK4WlLNe@A*kGzw&&=692r<^K(mlKag7E z_c<;Zodafxe_!UUpIG8A>)l6_`Ahd#E%9wd_nFDO*8MfhjDF-kE15sIziyco-n%bi znH6iezhRk8w!1HXp3HxCf73Es=en<%%un3kvdo-p_l=TyMQW7D`GK3}mf7dN_q=VH zqd#-s!7_6jr+VgYcGKB1C$93IcPw-AQ}?WN%_>3UhQ}a&&ldWo8ODH8?RfISM5uMNdWw<2FLf diff --git a/resources/VanDoornDissertation/dissertation.tex b/resources/VanDoornDissertation/dissertation.tex index fce8139..05e9ace 100644 --- a/resources/VanDoornDissertation/dissertation.tex +++ b/resources/VanDoornDissertation/dissertation.tex @@ -1,5 +1,5 @@ \RequirePackage{fix-cm} -\def\OPTpagesize{4.8in,7.9in} % Page size +\def\OPTpagesize{6in,9in} % Page size \documentclass[12pt]{report} \usepackage[hyphens]{url} \usepackage[ diff --git a/src/CubicalHottBook/Chapter2.lagda.md b/src/CubicalHottBook/Chapter2.lagda.md index caf94c5..f9b0c0d 100644 --- a/src/CubicalHottBook/Chapter2.lagda.md +++ b/src/CubicalHottBook/Chapter2.lagda.md @@ -16,8 +16,8 @@ transportconst : {A : Type l} {x y : A} → (B : Type l2) → (p : x ≡ y) → (b : B) - → subst ? p ? ≡ ? -transportconst B p b = ? + → subst (λ _ → B) p b ≡ b +transportconst B p b i = {! !} ``` ### Definition 2.4.1 @@ -58,7 +58,6 @@ mkIsEquiv : {A B : Type} {f : A → B} mkIsEquiv {B = B} {f = f} g forward backward = record { equiv-proof = eqv-prf } where postulate helper : (y : B) → (z : fiber f y) → (g y , forward y) ≡ z - -- helper y (x , p) = Σ-≡,≡→≡ (ap g (sym p) ∙ backward x , {! !}) eqv-prf : (y : B) → isContr (fiber f y) eqv-prf y = (g y , forward y) , helper y @@ -67,22 +66,22 @@ mkIsEquiv {B = B} {f = f} g forward backward = record { equiv-proof = eqv-prf } ### Theorem 2.11.3 ``` -theorem2∙11∙3 : {A B : Type} {f g : A → B} {a a' : A} - → (p : a ≡ a') - → (q : f a ≡ g a) - → subst (λ x → f x ≡ g x) p q ≡ sym (ap f p) ∙ q ∙ ap g p -theorem2∙11∙3 refl q = sym (unitR q) +-- theorem2∙11∙3 : {A B : Type} {f g : A → B} {a a' : A} +-- → (p : a ≡ a') +-- → (q : f a ≡ g a) +-- → subst (λ x → f x ≡ g x) p q ≡ sym (ap f p) ∙ q ∙ ap g p +-- theorem2∙11∙3 refl q = sym (unitR q) ``` ### Theorem 2.11.5 ``` -postulate - theorem2∙11∙5 : {A : Type} {a a' : A} - → (p : a ≡ a') - → (q : a ≡ a) - → (r : a' ≡ a') - → (transport (λ x → x ≡ x) p q ≡ r) ≃ (q ∙ p ≡ p ∙ r) +-- postulate +-- theorem2∙11∙5 : {A : Type} {a a' : A} +-- → (p : a ≡ a') +-- → (q : a ≡ a) +-- → (r : a' ≡ a') +-- → (transport (λ x → x ≡ x) p q ≡ r) ≃ (q ∙ p ≡ p ∙ r) -- theorem2∙11∙5 {a = a} refl q r = f , mkIsEquiv g {! !} {! !} where -- f : (q ≡ r) → (q ∙ refl ≡ r) -- f refl = unitR q diff --git a/src/CubicalHottBook/Prelude.agda b/src/CubicalHottBook/Prelude.agda index 53e7450..60845ab 100644 --- a/src/CubicalHottBook/Prelude.agda +++ b/src/CubicalHottBook/Prelude.agda @@ -4,6 +4,9 @@ module CubicalHottBook.Prelude where open import Cubical.Foundations.Function public open import Data.Product.Properties public open import Cubical.Foundations.Prelude public -open import Cubical.Data.Equality public using (id) open import Cubical.Foundations.Equiv public +module Inductive where + open import Cubical.Data.Equality public + +open Inductive public using (id) diff --git a/src/HottBook/Chapter6.lagda.md b/src/HottBook/Chapter6.lagda.md index d8b59e5..4e6f455 100644 --- a/src/HottBook/Chapter6.lagda.md +++ b/src/HottBook/Chapter6.lagda.md @@ -480,6 +480,4 @@ module Pushout where Pushout : {A B C : Set} → (f : C → A) → (g : C → B) → Set syntax Pushout A B C = A ⊔[ C ] B -``` - -## asdf \ No newline at end of file +``` \ No newline at end of file diff --git a/src/VanDoornDissertation/HoTT/LongExactSequence.agda b/src/VanDoornDissertation/HoTT/LongExactSequence.agda new file mode 100644 index 0000000..b5c0d2a --- /dev/null +++ b/src/VanDoornDissertation/HoTT/LongExactSequence.agda @@ -0,0 +1,4 @@ +{-# OPTIONS --cubical --safe #-} + +module VanDoornDissertation.HoTT.LongExactSequence where +