Browse Source

Clean xhtml, convert to html5

master
Thierry 2 years ago
parent
commit
0233d55895
21 changed files with 25 additions and 25 deletions
  1. +1
    -1
      index.html
  2. +1
    -1
      younotes1/1.1-motivation-philosophy.html
  3. +1
    -1
      younotes1/1.2-what-is-a-category.html
  4. +1
    -1
      younotes1/10.1-monads.html
  5. +1
    -1
      younotes1/10.2-monoid-in-the-category-of-endofunctors.html
  6. +1
    -1
      younotes1/2.1-functions-epimorphisms.html
  7. +1
    -1
      younotes1/2.2-monomorphisms-simple-types.html
  8. +1
    -1
      younotes1/3.1-examples-orders-monoids.html
  9. +3
    -3
      younotes1/3.2-kleisli-category.html
  10. +1
    -1
      younotes1/4.1-terminal-and-initial-objects.html
  11. +2
    -2
      younotes1/4.2-products.html
  12. +1
    -1
      younotes1/5.1-coproducts-sum-types.html
  13. +1
    -1
      younotes1/5.2-algebraic-data-types.html
  14. +1
    -1
      younotes1/6.1-functors.html
  15. +2
    -2
      younotes1/6.2-functors-in-programming.html
  16. +1
    -1
      younotes1/7.1-functoriality-bifunctors.html
  17. +1
    -1
      younotes1/7.2-monoidal-categories-functoriality-of-adts-profunctors.html
  18. +1
    -1
      younotes1/8.1-function-objects-exponentials.html
  19. +1
    -1
      younotes1/8.2-type-algebra-curry-howard-lambek-isomorphism.html
  20. +1
    -1
      younotes1/9.1-natural-transformations.html
  21. +1
    -1
      younotes1/9.2-bicategories.html

+ 1
- 1
index.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/1.1-motivation-philosophy.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>1.1: Motivation and Philosophy | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/1.2-what-is-a-category.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>1.2: What is a category | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/10.1-monads.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>10.1: Monads | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/10.2-monoid-in-the-category-of-endofunctors.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>10.2: Monoid in the category of endofunctors | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/2.1-functions-epimorphisms.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>2.1: Functions, epimorphisms | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/2.2-monomorphisms-simple-types.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>2.2: Monomorphisms, simple types | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/3.1-examples-orders-monoids.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>3.1: Examples of categories, orders, monoids | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 3
- 3
younotes1/3.2-kleisli-category.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>3.2: Kleisli category | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>
@@ -40,8 +40,8 @@ This deals with an interesting case to study.
<br>This is not a total order because there may exist disjoint sets or sets that partially overlap.
<br>We can have a diamond situation :
<div class="flex-wrap">
<img class="margin border" src="img/diamond1.jpg" alt="" />
<img class="margin border" src="img/diamond2.jpg" alt="" />
<img class="margin border" src="img/diamond1.jpg" alt="">
<img class="margin border" src="img/diamond2.jpg" alt="">
</div>

We have a category based on sets where the arrows are not functions, but relations. Some versions of this category is used in modeling topology ; open sets have this property of inclusion.


+ 1
- 1
younotes1/4.1-terminal-and-initial-objects.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>4.1: Terminal and initial objects | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 2
- 2
younotes1/4.2-products.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>4.2: Products | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>
@@ -119,7 +119,7 @@ We say that <code>c</code> is better than <code>c'</code> if there is a unique m
<br>The definition of product is :

<div class="flex-wrap">
<img class="margin border" src="img/product4.jpg" alt="Cartesian product 4" />
<img class="margin border" src="img/product4.jpg" alt="Cartesian product 4">
<div class="inline-block border margin padding">
A categorical product of two objects <code>a</code> and <code>b</code> is a third object <code>c</code> with two projections


+ 1
- 1
younotes1/5.1-coproducts-sum-types.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>5.1: Coproducts, sum types | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/5.2-algebraic-data-types.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>5.2: Algebraic data types | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/6.1-functors.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>6.1: Functors | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 2
- 2
younotes1/6.2-functors-in-programming.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>6.2: Functors in programming | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>
@@ -61,7 +61,7 @@ We need to prove that <pre>fmap id<sub>a</sub> = id<sub>Maybe a</sub></pre>
We need to prove that
<pre>fmap(g . f) = fmap g . fmap f</pre>
Corresponds to this diagram :
<div><img class="margin border" src="img/fmap-composition.jpg" alt="fmap composition" /><br>(TODO : add <code>fmap g . fmap f</code>)</div>
<div><img class="margin border" src="img/fmap-composition.jpg" alt="fmap composition"><br>(TODO : add <code>fmap g . fmap f</code>)</div>
This can be showed by equational reasoning using the same method as we did for identity (It's done on the <a href="https://bartoszmilewski.com/2015/01/20/functors/">blog page about functors</a>).
<br>Strictly speaking there is no need to prove it because as we use parametric polymorphism, this is a theorem for free. Once the id property is proven, this follows.



+ 1
- 1
younotes1/7.1-functoriality-bifunctors.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>7.1: Functoriality, bifunctors | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/7.2-monoidal-categories-functoriality-of-adts-profunctors.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>7.2: Monoidal Categories, Functoriality of ADTs, Profunctors | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/8.1-function-objects-exponentials.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>8.1: Function objects, exponentials | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/8.2-type-algebra-curry-howard-lambek-isomorphism.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>8.2: Type algebra, Curry-Howard-Lambek isomorphism | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/9.1-natural-transformations.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>9.1: Natural transformations | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


+ 1
- 1
younotes1/9.2-bicategories.html View File

@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta charset="utf-8">
<title>9.2: bicategories | Categories Bartosz Milewski Youtube notes</title>
<link rel="shortcut icon" href="favicon.png" type="image/x-icon">
<link rel="copyright" href="http://www.gnu.org/copyleft/gpl.html"/>


Loading…
Cancel
Save