From 4b5cd69a660df4ea2aea4aee378ea769e851cb81 Mon Sep 17 00:00:00 2001 From: Michael Zhang Date: Fri, 24 May 2024 22:54:13 -0500 Subject: [PATCH] push --- .editorconfig | 3 + .gitignore | 1 + Makefile | 4 +- html/book.toml | 12 ++- html/src/SUMMARY.md | 6 ++ html/src/front.md | 22 ++++- html/src/hott-front.md | 3 + resources/MayConcise/ConciseRevised.pdf | Bin 1218573 -> 0 bytes resources/VanDoornDissertation/.gitignore | 3 + .../VanDoornDissertation/dissertation.pdf | Bin 1328373 -> 763964 bytes .../VanDoornDissertation/dissertation.tex | 31 ++++-- src/MayConcise/Chapter1.lagda.md | 20 ++++ src/VanDoornDissertation/HIT.lagda.md | 29 ++++++ .../Preliminaries.lagda.md | 89 ++++++++++++++++++ 14 files changed, 209 insertions(+), 14 deletions(-) create mode 100644 .editorconfig create mode 100644 html/src/hott-front.md delete mode 100644 resources/MayConcise/ConciseRevised.pdf create mode 100644 resources/VanDoornDissertation/.gitignore create mode 100644 src/MayConcise/Chapter1.lagda.md create mode 100644 src/VanDoornDissertation/HIT.lagda.md create mode 100644 src/VanDoornDissertation/Preliminaries.lagda.md diff --git a/.editorconfig b/.editorconfig new file mode 100644 index 0000000..3f999da --- /dev/null +++ b/.editorconfig @@ -0,0 +1,3 @@ +[*] +indent_size = 2 +indent_style = space \ No newline at end of file diff --git a/.gitignore b/.gitignore index 171a389..4ecff1c 100644 --- a/.gitignore +++ b/.gitignore @@ -1 +1,2 @@ *.agdai +.DS_Store \ No newline at end of file diff --git a/Makefile b/Makefile index 7429825..94aec3c 100644 --- a/Makefile +++ b/Makefile @@ -1,7 +1,7 @@ GENDIR := html/src/generated build-to-html: - find src/HottBook \( -name "*.agda" -o -name "*.lagda.md" \) -print0 \ + find src \( -name "*.agda" -o -name "*.lagda.md" \) -print0 \ | rust-parallel -0 agda \ --html \ --html-dir=$(GENDIR) \ @@ -17,6 +17,6 @@ refresh-book: build-to-html mdbook serve html deploy: build-book - rsync -azrP html/book/ root@veil:/home/blogDeploy/public/hott-book + rsync -azrP html/book/ root@veil:/home/blogDeploy/public/research .PHONY: build-book build-to-html deploy \ No newline at end of file diff --git a/html/book.toml b/html/book.toml index b2e68ce..0a591a2 100644 --- a/html/book.toml +++ b/html/book.toml @@ -13,12 +13,16 @@ macros = "./macros.txt" [preprocessor.chapter-zero] levels = [0] +[preprocessor.graphviz] +command = "mdbook-graphviz" +output-to-file = false + [output.html] additional-js = [ - # "theme/pagetoc.js" + # "theme/pagetoc.js" ] additional-css = [ - "Agda.css", - "style.css", - # "theme/pagetoc.css" + "Agda.css", + "style.css", + # "theme/pagetoc.css" ] diff --git a/html/src/SUMMARY.md b/html/src/SUMMARY.md index d48f08f..3ff1b1a 100644 --- a/html/src/SUMMARY.md +++ b/html/src/SUMMARY.md @@ -1,6 +1,9 @@ # Summary - [Front](./front.md) + +# HoTT Book + - [Chapter 1](./generated/HottBook.Chapter1.md) - [Exercises](./generated/HottBook.Chapter1Exercises.md) - [Chapter 2](./generated/HottBook.Chapter2.md) @@ -16,3 +19,6 @@ - [Definition 3.3.1](./generated/HottBook.Chapter3Definition331.md) - [Lemma 3.3.3](./generated/HottBook.Chapter3Lemma333.md) +# Van Doorn Dissertation + +- [Preliminaries](./generated/VanDoornDissertation.Preliminaries.md) \ No newline at end of file diff --git a/html/src/front.md b/html/src/front.md index ebc280d..24f68fb 100644 --- a/html/src/front.md +++ b/html/src/front.md @@ -1,6 +1,24 @@ -# Homotopy Type Theory +# Research -I'm recreating a formalization for the Homotopy Type Theory book as I'm working through it to help me learn. +This book tracks my current research goals and progress. - [Source](https://git.mzhang.io/school/type-theory) +```dot process +digraph { + rankdir="BT" + + subgraph cluster_exploration { + label = "random cloud of exploration" { + mayconcise [label="concise course" URL="https://git.mzhang.io/school/type-theory/raw/branch/master/resources/MayConcise/ConciseRevised.pdf"] + hott [label = "hott book" URL="https://hott.github.io/book/hott-ebook.pdf.html"] + } + } + + subgraph cluster_thesis { + label = "thesis" { + + } + } +} +``` \ No newline at end of file diff --git a/html/src/hott-front.md b/html/src/hott-front.md new file mode 100644 index 0000000..00ea72d --- /dev/null +++ b/html/src/hott-front.md @@ -0,0 +1,3 @@ +# Homotopy Type Theory + +I'm recreating a formalization for the Homotopy Type Theory book as I'm working through it to help me learn. diff --git a/resources/MayConcise/ConciseRevised.pdf b/resources/MayConcise/ConciseRevised.pdf deleted file mode 100644 index f17fd9df3cab7bb75b482a497bf6f075b6c507d0..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1218573 zcma&NL$EMFlPr4l9ox2T+qP}nwr$(CZQHhOw27^mvpGH^10ydl zq?5CwiGdBI`=*Kf%p?#4bhn>e0@`|JUnz|^Tp;9ba8Cr-+R4-Lz*}E>XIG#kghgqR zMCm;M(6dlHdb7HCiEz->PD9q1Z|s)b?sNSnLOiHKk>UKGP#Jcl;&eYYJ&KbvcMXC? zc@FUlmY$_pE)l`y`OAI=!i-RR!(kK)!!$7 zOhG{bKvZafCkF>~7GH#OVUOMze15%nyFF|{1R=wu_x69>_VWEhI1PlN!3Vz&b9gPG 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\RequirePackage{fix-cm} +\def\OPTpagesize{4.8in,7.9in} % Page size \documentclass[12pt]{report} \usepackage[hyphens]{url} -\usepackage{hyperref} -\usepackage[margin=1.2in]{geometry} -\pdfoutput=1 +\usepackage[ + backref=page, + colorlinks, + citecolor=linkcolor, + linkcolor=linkcolor, + urlcolor=linkcolor, + unicode, +]{hyperref} +\usepackage[ + papersize={\OPTpagesize}, + margin=0.4in, + twoside, + includehead, +]{geometry} +% \pdfoutput=1 \usepackage{lmodern} \usepackage[utf8x]{inputenc} \usepackage[T1]{fontenc} -\usepackage{amsmath,mathtools,amssymb,etoolbox,enumerate,xspace} +\usepackage{amsmath,amsfonts,mathtools,amssymb,etoolbox,enumerate,xspace} \usepackage{microtype} +\usepackage{ctex} \usepackage{caption,subcaption} \mathtoolsset{mathic,centercolon} \usepackage[numbered]{bookmark} +\def\OPTlinkcolor{0,0.45,0} % RGB components for clickable links + % footnotes numbered consecutively throughout chapters \usepackage{chngcntr} \counterwithout{footnote}{chapter} %% URL \usepackage{xcolor} +\definecolor{linkcolor}{rgb}{\OPTlinkcolor} \usepackage{cleveref} \hypersetup{ colorlinks, @@ -45,6 +62,8 @@ \protected\def\tikz@nonactivecolon{\ifmmode\mathrel{\mathop\ordinarycolon}\else:\fi} \makeatother +\linespread{1.05} % Palatino looks better with this + %% Lean code @@ -85,7 +104,7 @@ %\renewcommand{\kappa}{\varkappa} % \renewcommand{\rho}{\varrho} \renewcommand{\phi}{\varphi} -\renewcommand{\C}{\mathbb{C}} +\newcommand{\C}{\mathbb{C}} \newcommand{\br}[1]{\langle#1\rangle} @@ -172,7 +191,7 @@ % \newcommand{\isprop}{\textnormal{is-prop}} % \newcommand{\prop}{\textnormal{Prop}} % \newcommand{\isset}{\textnormal{is-set}} -\renewcommand{\U}{\UU} +\newcommand{\U}{\UU} % \newcommand{\type}{\mathcal{U}} % \newcommand{\set}{\textnormal{set}} % \newcommand{\fa}[2]{\ensuremath{\Pi(#1),\ #2}} diff --git a/src/MayConcise/Chapter1.lagda.md b/src/MayConcise/Chapter1.lagda.md new file mode 100644 index 0000000..0c6fc2e --- /dev/null +++ b/src/MayConcise/Chapter1.lagda.md @@ -0,0 +1,20 @@ +``` +{-# OPTIONS --cubical #-} +module MayConcise.Chapter1 where +``` + +## 1 What is algebraic topology? + +https://en.wikipedia.org/wiki/Homomorphism + +> A homomorphism is a map between two algebraic structures of the same type (that is of the same name), that preserves the operations of the structures. This means a map f : A → B {\displaystyle f:A\to B} between two sets A {\displaystyle A}, B {\displaystyle B} equipped with the same structure such that, if ⋅ {\displaystyle \cdot } is an operation of the structure (supposed here, for simplification, to be a binary operation), then +> +> ``` +> f ( x ⋅ y ) = f ( x ) ⋅ f ( y ) {\displaystyle f(x\cdot y)=f(x)\cdot f(y)} +> ``` +> +> for every pair x {\displaystyle x}, y {\displaystyle y} of elements of A {\displaystyle A}. + +``` +homotopy : {X Y : Set} {p q : X → Y} +``` \ No newline at end of file diff --git a/src/VanDoornDissertation/HIT.lagda.md b/src/VanDoornDissertation/HIT.lagda.md new file mode 100644 index 0000000..790c903 --- /dev/null +++ b/src/VanDoornDissertation/HIT.lagda.md @@ -0,0 +1,29 @@ +``` +{-# OPTIONS --cubical #-} +module VanDoornDissertation.HIT where + +open import Data.Nat +open import VanDoornDissertation.Preliminaries +``` + +# 3 Higher Inductive Types + +## 3.1 Propositional Truncation + +``` +data one-step-truncation (A : Set) : Set where + f : A → one-step-truncation A + e : (x y : A) → f x ≡ f y + +weakly-constant : {A B : Set} → (g : A → B) → Set +weakly-constant {A} g = {x y : A} → g x ≡ g y + +definition3∙1∙1 : {A : Set} → one-step-truncation A → ℕ → Set +definition3∙1∙1 {A} trunc zero = A +definition3∙1∙1 {A} trunc (suc n) = one-step-truncation (definition3∙1∙1 trunc n) + +fs : {A : Set} → one-step-truncation A → (n : ℕ) → Set +fs trunc n = (definition3∙1∙1 trunc n) → (definition3∙1∙1 trunc (suc n)) + +-- lemma3∙1∙3 : {X : Set} → {x : X} → is +``` \ No newline at end of file diff --git a/src/VanDoornDissertation/Preliminaries.lagda.md b/src/VanDoornDissertation/Preliminaries.lagda.md new file mode 100644 index 0000000..7ac242f --- /dev/null +++ b/src/VanDoornDissertation/Preliminaries.lagda.md @@ -0,0 +1,89 @@ +``` +{-# OPTIONS --cubical #-} +module VanDoornDissertation.Preliminaries where + +open import Agda.Primitive +open import Agda.Primitive.Cubical +``` + +### 2.2.1 Paths + +``` +Path : {ℓ : Level} (A : Set ℓ) → A → A → Set ℓ +Path A = PathP (λ i → A) + +infix 4 _≡_ +_≡_ : {ℓ : Level} {A : Set ℓ} → A → A → Set ℓ +_≡_ {A = A} = Path A + +private + to-path : {ℓ : Level} {A : Set ℓ} → (f : I → A) → Path A (f i0) (f i1) + to-path f i = f i +refl : {ℓ : Level} {A : Set ℓ} {x : A} → x ≡ x +refl {x = x} = to-path (λ i → x) + +id : {l : Level} {A : Set l} → A → A +id x = x + +ap : {l1 l2 : Level} {A : Set l1} {B : Set l2} {x y : A} + → (f : A → B) + → (p : x ≡ y) + → f x ≡ f y +ap {l1} {l2} {A} {B} {x} {y} f p i = f (p i) + -- J (λ x y p → f x ≡ f y) (λ x → refl) x y p + +transport : {l₁ l₂ : Level} {A : Set l₁} {x y : A} + → (P : A → Set l₂) + → (p : x ≡ y) + → P x → P y +transport {l₁} {l₂} {A} {x} {y} P p = primTransp (λ i → P (p i)) i0 +``` + +### 2.2.3 More on paths + +#### Pathovers + +``` +dependent-path : {A : Set} + → (P : A → Set) + → {x y : A} + → (p : x ≡ y) + → (u : P x) → (v : P y) → Set +dependent-path P p u v = transport P p u ≡ v + +syntax dependent-path P p u v = u ≡[ P , p ] v + +-- https://git.mzhang.io/school/type-theory/issues/16 +apd : ∀ {a b} {A : I → Set a} {B : (i : I) → A i → Set b} + → (f : (i : I) → (a : A i) → B i a) + → {x : A i0} + → {y : A i1} + → (p : PathP A x y) + → PathP (λ i → B i (p i)) (f i0 x) (f i1 y) +apd f p i = f i (p i) +``` + +#### Squares + +``` +data square {A : Set} {a00 : A} : {a20 a02 a22 : A} + → a00 ≡ a20 + → a02 ≡ a22 + → a00 ≡ a02 + → a20 ≡ a22 + → Set + where + reflₛ : square refl refl refl refl +``` + +#### Squareovers and cubes + +``` + +``` + +#### Paths in type formers + +``` + +``` \ No newline at end of file

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