update

categories.html

@@ -41,6 +41,7 @@
 \(\newcommand{\id}{\mathrm{id}}\)
 \(\newcommand{\ob}[1]{\mathrm{ob}(#1)}\)
 \(\newcommand{\hom}[1]{\mathrm{hom}(#1)}\)
+\(\newcommand{\Set}{\mathbf{Set}}\)
 </div>
 
 
@@ -212,15 +213,22 @@
 <p>Young field: <b>1942–45</b>, Samuel Eilenberg <span class="and"><span class="and">&amp;</span></span> Saunders Mac Lane
 </section>
 <section class="slide">
-<h2>Plan</h2>
-<ul style="font-size: 2em">
-    <li>Why?</li>
-    <li class="yellow">What?</li>
-    <li>How?</li>
+<h2>Type Theory ⇒ Categories</h2>
+
+<ul>
+    <li>Type theory helped to remove paradoxes in Set Theory.</li>
+    <li>Prevent relations between different kind of objects.</li>
+    <li>Used in computer science</li>
+</ul>
+
+<ul>
+    <li>typed λ-calculus ⇒ cartesian closed categories</li>
+    <li>untyped λ-calculus ⇒ C-monoids (subclass of categories)</li>
+    <li>Martin-Löf type theories ⇒ locally cartesian closed categories</li>
 </ul>
 </section>
 <section class="slide">
-<h2>Definition: Category</h2>
+<h2>Category Definition</h2>
 
 <p> A Category \(\mathcal{C}\) is defined by:</p>
 <ul>
@@ -231,30 +239,43 @@
 </ul>
 </section>
 <section class="slide">
-<h2>Definition: Category</h2>
-
-<div style="position:relative">
-    <img               src="img/mp/objects.png"   alt="objects"   style="position:absolute;top:0;"/>
-    <img class="slide" src="img/mp/morphisms.png" alt="morphisms" style="position:absolute;top:0;"/>
-</div>
+<h2>Plan</h2>
+<ul style="font-size: 2em">
+    <li>Why?</li>
+    <li class="yellow">What?</li>
+    <li>How?</li>
+</ul>
 </section>
 <section class="slide">
-	<h2>Definition: Category [Composition]</h2>
+<h2>Category Definition: Objects</h2>
+
+<img src="img/mp/objects.png" alt="objects" />
+
+<p>\(\ob{\mathcal{C}}\) is a collection</p>
+</section>
+<section class="slide">
+<h2>Category Definition: Morphisms</h2>
+
+<img src="img/mp/morphisms.png" alt="morphisms"/>
+
+<p>\(\hom{A,B}\) is a collection</p>
+</section>
+<section class="slide">
+<h2>Category Definition: Composition</h2>
 <p>Composition (∘): \(f:A\rightarrow B, g:B\rightarrow C\)
     $$g\circ f:A\rightarrow C$$
 </p>
 <img src="img/mp/composition.png" alt="composition"/>
 </section>
 <section class="slide">
-	<h2>Definition: Category [Laws]</h2>
-<ul>
-    <li>for all \(X\), there is an \(\id_X\), s.t. for all \(f:A\to B\)
-        <img src="img/mp/identity.png" alt="identity"/>
-    </li>
-    <li> Composition is associative:
-    <img src="img/mp/associativecomposition.png" alt="associative composition"/>
-    </li>
-</ul>
+<h2>Category laws: neutral element</h2>
+<p>for all \(X\), there is an \(\id_X\), s.t. for all \(f:A\to B\):</p>
+<img src="img/mp/identity.png" alt="identity"/>
+</section>
+<section class="slide">
+<h2>Category laws: Associativity</h2>
+<p> Composition is associative:</p>
+<img src="img/mp/associativecomposition.png" alt="associative composition"/>
 </section>
 <section class="slide">
 <h2>Can this be a category? <span style="font-size: .5em">(\(\id_X\) implicit)</span></h2>
@@ -293,6 +314,36 @@
 </figure>
 </section>
 <section class="slide">
+<h2>Categories Everywhere?</h2>
+
+<h3>\(\Set\)</h3>
+<ul>
+    <li> \(\ob{\Set}\) are sets</li>
+    <li> \(\hom{\Set}\) are functions</li>
+    <li> ∘ is functions composition </li>
+</ul>
+
+<ul class="slide">
+    <li>\(\ob{\Set}\) is a proper class ; not a set</li>
+    <li>\(\hom{E,F}\) is a set</li>
+    <li>\(\Set\) is a <em>locally small category</em></li>
+</ul>
+</section>
+<section class="slide">
+<h2>Categories Everywhere?</h2>
+
+<h3>Strings</h3>
+<ul>
+    <li> \(\ob{Str}\) is a singleton </li>
+    <li> \(\hom{Str}\) each string </li>
+    <li> ∘ is concatenation <code>(++)</code> </li>
+</ul>
+<ul>
+    <li> <code>"" ++ u = u = u ++ ""</code> </li>
+    <li> <code>(u ++ v) ++ w = u ++ (v ++ w)</code> </li>
+</ul>
+</section>
+<section class="slide">
 <h2>Definition: Functor</h2>
 
 <p> A functor is a mapping between two categories.
@@ -317,12 +368,12 @@ A <em>functor</em> \(\F\) from \(\C\) to \(\D\):</p>
 <section class="slide">
 <h2>Functor: Example</h2>
 
-<img src="img/mp/functor-morphism.png" alt="Functor Morphisms"/>
+<img src="img/mp/functor-morphism.png" alt="Functor"/>
 </section>
 <section class="slide">
 <h2>Functor: Example</h2>
 
-<img src="img/mp/functor-morphism-color.png" alt="Functor Morphisms"/>
+<img src="img/mp/functor-morphism-color.png" alt="Functor"/>
 </section>
 <!-- End slides. -->
 

categories/00_Introduction/010_.html.bak

@@ -0,0 +1,12 @@
+<h1>Category Theory <span class="and">&amp;</span> Programming
+    <div><author style="font-size: .4em"><em class="base01">by</em> Yann Esposito
+        <div>
+            <twitter style="font-size: .5em">
+                <a href="http://twitter.com/yogsototh">@yogsototh</a>,
+            </twitter>
+            <googleplus style="font-size: .5em">
+                <a href="https://plus.google.com/117858550730178181663">+yogsototh</a>
+            </googleplus>
+        </div>
+    </author></div>
+</h1>

categories/00_Introduction/020_Plan.html.bak

@@ -0,0 +1,6 @@
+<h2>Plan</h2>
+<ul style="font-size: 2em">
+    <li class="yellow">Why?</li>
+    <li>What?</li>
+    <li>How?</li>
+</ul>

categories/00_Introduction/030_Abstraction_Example.html

@@ -0,0 +1,17 @@
+<h2>Abstraction Example</h2>
+<p>Something you see very often but in different instances.</p>
+<div class="slide">
+    <p>Numbers: 1,2,3,...  <em class="small">3400 BC, real numbers 760 BC</em></p>
+    <figure class="left">
+        <img src="categories/img/tally-count.png" style="height:3.8em" alt="Aboriginal Tally System"/>
+        <figcaption>Aboriginal Tally System</figcaption>
+    </figure>
+    <figure class="left">
+        <img src="categories/img/first-real-numbers.png" style="height:3.8em" alt="Mesopotamian Numbers"/>
+        <figcaption>Mesopotamian base 60 system</figcaption>
+    </figure>
+    <figure class="left">
+    <div class="likeimg" style="height:3.8em;margin-bottom: 1em"><span style="font-size: 3em">&nbsp;0&nbsp;</span></div>
+        <figcaption>Zero</figcaption>
+    </figure>
+    <div class="flush"></div>

categories/00_Introduction/040_Abstraction_Example_Numbers.html.bak

@@ -0,0 +1,14 @@
+<h2>Abstraction Example: Numbers</h2>
+<p>Many different things can be understood with numbers</p>
+<ul>
+    <li>How many apple, goats?</li>
+    <li>Distance</li>
+    <li>Time</li>
+    <li>...</li>
+</ul>
+<p>Manipulated with operators: 
+    <span class="yellow">=</span>,
+    <span class="yellow">&lt;</span>,
+    <span class="yellow">&gt;</span>,
+    <span class="yellow">+</span>,
+    <span class="yellow">×</span>, ...</p>

categories/00_Introduction/050_Abstraction_Example_Numbers.html

@@ -0,0 +1,5 @@
+<h2>Abstraction Example: Numbers</h2>
+<h3>Generalization: rational numbers</h3>
+<p>Rational numbers: \(\frac{p}{q}\) (concept is prehistoric): more precise.</p>
+<img src="categories/img/egyptian-hieroglyphics.jpg" alt="Egyptian Fractions"/>
+</div>

categories/00_Introduction/060_Abstraction_Example_Numbers.html

@@ -0,0 +1,4 @@
+<h2>Abstraction Example: Numbers</h2>
+<h3>Generalization: negative numbers</h3>
+<p>Negative numbers: ..., -3, -2, -1, 0, 1, 2, ... (100-50 BC): Debts, temperature</p>
+<img src="categories/img/negative-numbers.jpg" alt="Negative Numbers (Chinese)"/>

categories/00_Introduction/070_Abstraction_Example_Numbers.html.bak

@@ -0,0 +1,4 @@
+<h2>Abstraction Example: Numbers</h2>
+<h3>Generalization: Irrational Numbers</h3>
+<p>Irrational numbers: \(\mathbb{A}\), \(\mathbb{R}\) (500 BC → Pythogoras killed Hippasus because of \(\sqrt{2}\)!)</p>
+<p>Complex numbers: \(\mathbb{C}\) (100 AD, then 16th century)</p>

categories/00_Introduction/080_Abstraction_Example_Numbers.html.bak

@@ -0,0 +1,6 @@
+<h2>Abstraction Example: Numbers</h2>
+<h3>Generalization</h3>
+<ul>
+<li>More things enter into the notion</li>
+<li>More operator to manipulate the notion</li>
+</ul>

categories/00_Introduction/090_Numbers_Sets.html.bak

@@ -0,0 +1,30 @@
+	<h2>Numbers ⇒ Sets</h2>
+<table>
+<tr>
+    <th>Numbers</th>
+    <th>Set Theory (∞)/Abstract Algebra/Topology</th>
+</tr>
+<tr>
+    <td>\(\mathbb{N}\): \((+,0)\)</td>
+    <td>Semigroups</td>
+</tr>
+<tr>
+    <td>\(\mathbb{Z}\): \((+,0,\times,1)\)</td>
+    <td>Rings</td>
+</tr>
+<tr>
+    <td>\(\mathbb{Q}\)</td>
+    <td>Fields</td>
+</tr>
+<tr>
+    <td>\(\mathbb{R}\)</td>
+    <td>Complete Fields (<em class="base01">topology</em>)</td>
+</tr>
+<tr>
+    <td>\(\mathbb{C}\)</td>
+    <td>Algebræ</td>
+</tr>
+<tr><td></td><td>Modules,Vector Spaces, Monoids, ...</td></tr>
+</table>
+<p><span class="and" style="visibility:hidden">&amp;</span> More <strong>general</strong>: more things are sets.<br/>
+    <span class="and">&amp;</span> More <strong>precise</strong>: clear distinction between concepts.</p>

categories/00_Introduction/100_Sets_Categories.html.bak

@@ -0,0 +1,34 @@
+<h2>Sets ⇒? <span class="yellow">Categories</span></h2>
+<table>
+<tr>
+    <th>Numbers</th>
+    <th>Sets</th>
+    <th>Categories</th>
+</tr>
+<tr>
+    <td>\(\mathbb{N}\): \((+,0)\)</td>
+    <td>Semigroups</td>
+    <td>?</td>
+</tr>
+<tr>
+    <td>\(\mathbb{Z}\): \((+,0,\times,1)\)</td>
+    <td>Rings</td>
+    <td>?</td>
+</tr>
+<tr>
+    <td>\(\mathbb{Q}\)</td>
+    <td>Fields</td>
+    <td>?</td>
+</tr>
+<tr>
+    <td>\(\mathbb{R}\)</td>
+    <td>Complete Fields (<em class="base01">topology</em>)</td>
+    <td>?</td>
+</tr>
+<tr>
+    <td>\(\mathbb{C}\)</td>
+    <td>Algebræ</td>
+    <td>?</td>
+</tr>
+<tr><td></td><td>Modules,Vector Spaces, Monoids, ...</td><td>?</td></tr>
+</table>

categories/00_Introduction/110_Category_Theory.html.bak

@@ -0,0 +1,11 @@
+<h2><span class="yellow">/.*/</span> ⇒? Category Theory</h2>
+<p>Extend <span class="and">&amp;</span> Merge different scientific fields</p>
+<ul>
+<li>Topology</li>
+<li>Quantum Physics</li>
+<li>Logic</li>
+<li><b>Programming</b></li>
+</ul>
+<p><span class="and" style="visibility:hidden">&amp;</span> More <strong>general</strong>: more things are Categories.<br/>
+    <span class="and">&amp;</span> More <strong>precise</strong>: better distinction between concepts.</p>
+<p>Young field: <b>1942–45</b>, Samuel Eilenberg <span class="and">&amp;</span> Saunders Mac Lane

categories/00_Introduction/120_Type_Theory_Categories.html

@@ -0,0 +1,13 @@
+<h2>Type Theory ⇒ Categories</h2>
+
+<ul>
+    <li>Type theory helped to remove paradoxes in Set Theory.</li>
+    <li>Prevent relations between different kind of objects.</li>
+    <li>Used in computer science</li>
+</ul>
+
+<ul>
+    <li>typed λ-calculus ⇒ cartesian closed categories</li>
+    <li>untyped λ-calculus ⇒ C-monoids (subclass of categories)</li>
+    <li>Martin-Löf type theories ⇒ locally cartesian closed categories</li>
+</ul>

categories/00_Introduction/120_Type_Theory_Categories.html.bak

@@ -0,0 +1,13 @@
+<h2>Type Theory ⇒ Categories</h2>
+
+<ul>
+    <li>Type theory helped to remove paradoxes in Set Theory.</li>
+    <li>Prevent relations between different kind of objects.</li>
+    <li>Used in computer science</li>
+</ul>
+
+<ul>
+    <li>typed λ-calculus ⇒ cartesian closed categories</li>
+    <li>untyped λ-calculus ⇒ C-monoids (subclass of categories)</li>
+    <li>Martin-Löf type theories ⇒ locally cartesian closed categories</li>
+</ul>

categories/01_What/010_Category_Definition.html

@@ -1,4 +1,4 @@
-<h2>Definition: Category</h2>
+<h2>Category Definition</h2>
 
 <p> A Category \(\mathcal{C}\) is defined by:</p>
 <ul>

categories/01_What/010_Category_Definition.html.bak

@@ -0,0 +1,9 @@
+<h2>Category Definition</h2>
+
+<p> A Category \(\mathcal{C}\) is defined by:</p>
+<ul>
+    <li> <em>Objects (\(\ob{C}\))</em>,</li>
+    <li> <em>Morphisms (\(\hom{C}\))</em>,</li>
+    <li> a <em>Composition law (∘)</em></li>
+    <li> obeying some <em>Properties</em>.</li>
+</ul>

categories/01_What/020_Plan.html.bak

@@ -0,0 +1,6 @@
+<h2>Plan</h2>
+<ul style="font-size: 2em">
+    <li>Why?</li>
+    <li class="yellow">What?</li>
+    <li>How?</li>
+</ul>

categories/01_What/030_Category_Definition_Objects.html

@@ -0,0 +1,5 @@
+<h2>Category Definition: Objects</h2>
+
+<img src="categories/img/mp/objects.png" alt="objects" />
+
+<p>\(\ob{\mathcal{C}}\) is a collection</p>

categories/01_What/030_Category_Definition_Objects.html.bak

@@ -0,0 +1,5 @@
+<h2>Category Definition: Objects</h2>
+
+<img src="img/mp/objects.png" alt="objects" />
+
+<p>\(\ob{\mathcal{C}}\) is a collection</p>

categories/01_What/040_Category_Definition_Morphisms.html

@@ -0,0 +1,5 @@
+<h2>Category Definition: Morphisms</h2>
+
+<img src="categories/img/mp/morphisms.png" alt="morphisms"/>
+
+<p>\(\hom{A,B}\) is a collection</p>

categories/01_What/040_Category_Definition_Morphisms.html.bak

@@ -0,0 +1,5 @@
+<h2>Category Definition: Morphisms</h2>
+
+<img src="img/mp/morphisms.png" alt="morphisms"/>
+
+<p>\(\hom{A,B}\) is a collection</p>

categories/01_What/050_Category_Definition_Composition.html

@@ -0,0 +1,5 @@
+<h2>Category Definition: Composition</h2>
+<p>Composition (∘): \(f:A\rightarrow B, g:B\rightarrow C\)
+    $$g\circ f:A\rightarrow C$$
+</p>
+<img src="categories/img/mp/composition.png" alt="composition"/>

categories/01_What/050_Category_Definition_Composition.html.bak

@@ -1,4 +1,4 @@
-	<h2>Definition: Category [Composition]</h2>
+<h2>Category Definition: Composition</h2>
 <p>Composition (∘): \(f:A\rightarrow B, g:B\rightarrow C\)
     $$g\circ f:A\rightarrow C$$
 </p>

categories/01_What/060_Category_laws_neutral_element.html

@@ -0,0 +1,3 @@
+<h2>Category laws: neutral element</h2>
+<p>for all \(X\), there is an \(\id_X\), s.t. for all \(f:A\to B\):</p>
+<img src="categories/img/mp/identity.png" alt="identity"/>

categories/01_What/060_Category_laws_neutral_element.html.bak

@@ -0,0 +1,3 @@
+<h2>Category laws: neutral element</h2>
+<p>for all \(X\), there is an \(\id_X\), s.t. for all \(f:A\to B\):</p>
+<img src="img/mp/identity.png" alt="identity"/>

categories/01_What/070_Category_laws_Associativity.html

@@ -0,0 +1,3 @@
+<h2>Category laws: Associativity</h2>
+<p> Composition is associative:</p>
+<img src="categories/img/mp/associativecomposition.png" alt="associative composition"/>

categories/01_What/070_Category_laws_Associativity.html.bak

@@ -0,0 +1,3 @@
+<h2>Category laws: Associativity</h2>
+<p> Composition is associative:</p>
+<img src="img/mp/associativecomposition.png" alt="associative composition"/>

categories/01_What/080_Can_this_be_a_category_id_X_implicit.html

@@ -0,0 +1,34 @@
+<h2>Can this be a category? <span style="font-size: .5em">(\(\id_X\) implicit)</span></h2>
+<figure class="left">
+    <img src="categories/img/mp/cat-example1.png" alt="Category example 1"/>
+    <figcaption class="slide">
+        <span class="green">OK</span>
+    </figcaption>
+</figure>
+<figure class="left">
+    <img src="categories/img/mp/cat-example2.png" alt="Category example 2"/>
+    <figcaption class="slide">
+        no candidate for \(g\circ f\)
+        <span class="red">NO</span>
+    </figcaption>
+</figure>
+<figure class="left">
+    <img src="categories/img/mp/cat-example3.png" alt="Category example 3"/>
+    <figcaption class="slide">
+    <span class="green">YES</span>
+    </figcaption>
+</figure>
+<figure class="left">
+    <img src="categories/img/mp/cat-example4.png" alt="Category example 4"/>
+    <figcaption class="slide">
+        no candidate for \(f:C\to B\)
+        <span class="red">NO</span>
+    </figcaption>
+</figure>
+<figure class="left">
+    <img src="categories/img/mp/cat-example5.png" alt="Category example 5"/>
+    <figcaption class="slide">
+        \((h∘g)∘f=\id_B∘f=f≠h=h∘\id_A=h∘(g∘f)\)
+        <span class="red">NO</span>
+    </figcaption>
+</figure>

categories/01_What/090_Categories_Everywhere.html

@@ -0,0 +1,14 @@
+<h2>Categories Everywhere?</h2>
+
+<h3>\(\Set\)</h3>
+<ul>
+    <li> \(\ob{\Set}\) are sets</li>
+    <li> \(\hom{\Set}\) are functions</li>
+    <li> ∘ is functions composition </li>
+</ul>
+
+<ul class="slide">
+    <li>\(\ob{\Set}\) is a proper class ; not a set</li>
+    <li>\(\hom{E,F}\) is a set</li>
+    <li>\(\Set\) is a <em>locally small category</em></li>
+</ul>

categories/01_What/090_Categories_Everywhere.html.bak

@@ -0,0 +1,14 @@
+<h2>Categories Everywhere?</h2>
+
+<h3>\(\Set\)</h3>
+<ul>
+    <li> \(\ob{\Set}\) are sets</li>
+    <li> \(\hom{\Set}\) are functions</li>
+    <li> ∘ is functions composition </li>
+</ul>
+
+<ul class="slide">
+    <li>\(\ob{\Set}\) is a proper class ; not a set</li>
+    <li>\(\hom{E,F}\) is a set</li>
+    <li>\(\Set\) is a <em>locally small category</em></li>
+</ul>

categories/01_What/100_Categories_Everywhere.html

@@ -0,0 +1,12 @@
+<h2>Categories Everywhere?</h2>
+
+<h3>Strings</h3>
+<ul>
+    <li> \(\ob{Str}\) is a singleton </li>
+    <li> \(\hom{Str}\) each string </li>
+    <li> ∘ is concatenation <code>(++)</code> </li>
+</ul>
+<ul>
+    <li> <code>"" ++ u = u = u ++ ""</code> </li>
+    <li> <code>(u ++ v) ++ w = u ++ (v ++ w)</code> </li>
+</ul>

categories/01_What/100_Categories_Everywhere.html.bak

@@ -0,0 +1,12 @@
+<h2>Categories Everywhere?</h2>
+
+<h3>Strings</h3>
+<ul>
+    <li> \(\ob{Str}\) is a singleton </li>
+    <li> \(\hom{Str}\) each string </li>
+    <li> ∘ is concatenation <code>(++)</code> </li>
+</ul>
+<ul>
+    <li> <code>"" ++ u = u = u ++ ""</code> </li>
+    <li> <code>(u ++ v) ++ w = u ++ (v ++ w)</code> </li>
+</ul>

categories/01_What/110_Definition_Functor.html.bak

@@ -0,0 +1,15 @@
+<h2>Definition: Functor</h2>
+
+<p> A functor is a mapping between two categories.
+Let \(\C\) and \(\D\) be two categories.
+A <em>functor</em> \(\F\) from \(\C\) to \(\D\):</p>
+<ul>
+    <li> Associate objects: \(A\in\ob{\C}\) to \(\F(A) \in\ob{\D}\) </li>
+    <li> Associate morphisms: \(f:A\to B\) to \(\F(f) : \F(A) \to \F(B)\)
+        such that
+        <ul>
+            <li>\( \F (\id_X) = \id_{\F(X)} \),</li>
+            <li>\( \F (g \circ_\C f) = \F(g) \circ_\D \F(f) \)</li>
+        </ul>
+    </li>
+</ul>

categories/01_What/120_Functor_Example.html

@@ -0,0 +1,3 @@
+<h2>Functor: Example</h2>
+
+<img src="categories/img/mp/functor.png" alt="Functor"/>

categories/01_What/130_Functor_Example.html

@@ -0,0 +1,3 @@
+<h2>Functor: Example</h2>
+
+<img src="categories/img/mp/functor-morphism.png" alt="Functor"/>

categories/01_What/130_Functor_Example.html.bak

@@ -0,0 +1,3 @@
+<h2>Functor: Example</h2>
+
+<img src="img/mp/functor-morphism.png" alt="Functor"/>

categories/01_What/140_Functor_Example.html

@@ -0,0 +1,3 @@
+<h2>Functor: Example</h2>
+
+<img src="categories/img/mp/functor-morphism-color.png" alt="Functor"/>

categories/01_What/140_Functor_Example.html.bak

@@ -0,0 +1,3 @@
+<h2>Functor: Example</h2>
+
+<img src="img/mp/functor-morphism-color.png" alt="Functor"/>

categories/gen

@@ -10,13 +10,16 @@ fi
 cd $scriptdir
 
 # Convert all slides from markdown
-for slide in slide-*.md(.N); do
+for slide in **/*.md(.N); do
     pandoc -f markdown -t html $slide > ${slide:r}.html
 done
 
 {
 cat head.html
-for slide in slide-*.html(.N); do
+for slide in **/*.html(.N); do
+    case $slide in
+        head.html|tail.html) continue
+    esac
     print -- '<section class="slide">'
     cat $slide | sed 's#&amp;#<span class="and">&</span>#g'
     print -- '</section>'

categories/head.html

@@ -41,6 +41,7 @@
 \(\newcommand{\id}{\mathrm{id}}\)
 \(\newcommand{\ob}[1]{\mathrm{ob}(#1)}\)
 \(\newcommand{\hom}[1]{\mathrm{hom}(#1)}\)
+\(\newcommand{\Set}{\mathbf{Set}}\)
 </div>
 
 

categories/img/mp/graph.mp

@@ -186,16 +186,19 @@ vardef nl_edge(expr posA,posB) =
     sub
 enddef;
 
-
-def drawloop(expr a,b,l) =
+vardef largeloop(expr a,b) =
     pair ba,ea;
     path circ,p,s;
     p:=a{1,1}..b..{1,-1}cycle;
-    circ:= fullcircle scaled 6 shifted a;
+    circ:= fullcircle scaled nodesize shifted a;
     ba = circ intersectionpoint (subpath (0,1) of p);
     ea = circ intersectionpoint (subpath (1,2) of p);
     s:= ba{1,1}..b..{1,-1}ea;
-    drawarrow s;
+    s
+enddef;
+
+def drawloop(expr a,b,l) =
+    drawarrow largeloop(a,b);
     label.top(l,b);
 enddef;
 

categories/img/mp/morphisms.mp

@@ -2,23 +2,33 @@
 z0=(0,0);
 z1=z0 shifted (gu,0);
 z2=z1 shifted (gu,0);
-z3=1/2[z0,z1] shifted (0,-gu);
-z4=1/2[z1,z2] shifted (0,-gu);
+z3=z2 shifted (gu,-0.5gu);
+z4=z3 shifted (gu,0);
 z5=z4 shifted (1.5u,0);
 z6=z5 shifted (2u,0);
 
+drawblock(z0,z6,btex $\mathcal{C}$ etex);
+
 drawState(z0, btex $A$ etex);
 drawState(z1, btex $B$ etex);
 drawState(z2, btex $C$ etex);
 
-drawoptions(withcolor base01);
 drawState(z3, btex $D$ etex);
+
+drawoptions(withcolor base01);
+drawarrow largeloop(z3,z3 shifted (0,3.8u)) dashed evenly;
+drawarrow largeloop(z3,z3 shifted (0,4u)) dashed evenly;
 drawState(z4, btex $E$ etex);
-draw z5 -- z6 dashed withdots withpen pencircle scaled 2bp;
-drawEdge(z3,z3, btex $id_D$ etex);
 drawEdge(z4,z4, btex $id_E$ etex);
+drawarrow edgeAngle(z3,z4,0) dashed evenly;
+drawarrow edgeAngle(z3,z4,20) dashed evenly;
+drawarrow edgeAngle(z3,z4,-20) dashed evenly;
+draw z5 -- z6 dashed withdots withpen pencircle scaled 2bp;
 
 drawoptions(withcolor yellow);
+drawarrow largeloop(z3,z3 shifted (0,3.5u)) dashed evenly;
+drawEdge(z3,z3, btex $id_D$ etex);
+drawloop(z3,z3 shifted (0,2.5u),btex $\ell$ etex);
 
 drawEdge(z0,z1, btex $f$ etex);
 drawEdgeWithAngle(z0,z1, btex $f'$ etex, 45);

categories/img/mp/objects.mp

@@ -1,17 +1,19 @@
-drawoptions(withcolor yellow);
 
 z0=(0,0);
 z1=z0 shifted (gu,0);
 z2=z1 shifted (gu,0);
-z3=1/2[z0,z1] shifted (0,-gu);
-z4=1/2[z1,z2] shifted (0,-gu);
+z3=z2 shifted (gu,-0.5gu);
+z4=z3 shifted (gu,0);
 z5=z4 shifted (1.5u,0);
 z6=z5 shifted (2u,0);
 
+drawblock(z0,z6,btex $\mathcal{C}$ etex);
+draw z5 -- z6 dashed withdots withpen pencircle scaled 2bp;
+
+drawoptions(withcolor yellow);
 drawState(z0, btex $A$ etex);
 drawState(z1, btex $B$ etex);
 drawState(z2, btex $C$ etex);
 
 drawState(z3, btex $D$ etex);
 drawState(z4, btex $E$ etex);
-draw z5 -- z6 dashed withdots withpen pencircle scaled 2bp;

categories/renameSlideFic.sh

@@ -0,0 +1,19 @@
+#!/usr/bin/env zsh
+
+i=10
+for fic in *.html; do
+    title=$( <$fic grep h2 | sed 's/<[^>]*>//g;s/[^a-zA-Z]/_/g;s/__*/_/g;s/^_//;s/_$//')
+    if ((i<100)); then
+        num="0$i"
+    else
+        num="$i"
+    fi
+    ((i+=10))
+    newfic=${num}_$title.${fic:e}
+    [[ $fic == $newfic ]] && { continue }
+    [[ -e $newfic ]] && {
+            print -- "$newfic already exists!" >&2
+            continue
+        }
+    mv $fic $newfic
+done

categories/slide-014.html

@@ -1,6 +0,0 @@
-<h2>Definition: Category</h2>
-
-<div style="position:relative">
-    <img               src="img/mp/objects.png"   alt="objects"   style="position:absolute;top:0;"/>
-    <img class="slide" src="img/mp/morphisms.png" alt="morphisms" style="position:absolute;top:0;"/>
-</div>

categories/slide-016.html

@@ -1,9 +0,0 @@
-	<h2>Definition: Category [Laws]</h2>
-<ul>
-    <li>for all \(X\), there is an \(\id_X\), s.t. for all \(f:A\to B\)
-        <img src="img/mp/identity.png" alt="identity"/>
-    </li>
-    <li> Composition is associative:
-    <img src="img/mp/associativecomposition.png" alt="associative composition"/>
-    </li>
-</ul>

categories/slide-020.html

@@ -1,3 +0,0 @@
-<h2>Functor: Example</h2>
-
-<img src="img/mp/functor-morphism.png" alt="Functor Morphisms"/>

categories/slide-021.html

@@ -1,3 +0,0 @@
-<h2>Functor: Example</h2>
-
-<img src="img/mp/functor-morphism-color.png" alt="Functor Morphisms"/>

themes/style/y/main.css

@@ -117,7 +117,7 @@
     border-right: none; }
   .deck-container ul {
     list-style: none; }
-  .deck-container .corps ul li:before {
+  .deck-container ul li:before {
     content: "- "; }
   .deck-container ol, .deck-container ul {
     padding-left: 0;

themes/style/y/main.sass

@@ -272,7 +272,7 @@ $secondTextColor: $base1
   ul
     list-style: none
 
-  .corps ul li:before
+  ul li:before
     content: "- "
 
   ol,ul