fixed sizes

This commit is contained in:
Yann Esposito (Yogsototh) 2012-12-10 22:20:14 +01:00
parent 765ff15e95
commit 67616fcc15
25 changed files with 68 additions and 38 deletions

View file

@ -94,7 +94,7 @@
</section>
<section class="slide">
<h2 id="general-overview">General Overview</h2>
<div style="float:right; width: 20%">
<div style="float:right; width: 18%">
<img src="categories/img/eilenberg.gif" alt="Samuel Eilenberg"/> <img src="categories/img/maclaine.jpg" alt="Saunders Mac Lane"/>
</div>
@ -262,7 +262,12 @@ such that for each \(f:A→B\):</p>
<section class="slide">
<h2>Question Time!</h2>
<img width="60%" src="categories/img/batquestion.jpg"/>
<figure style="width:70%; margin:0 auto">
<img src="categories/img/batquestion.jpg" width="100%"/>
<figcaption>
<em>- French-only joke -</em>
</figcaption>
</figure>
</section>
<section class="slide">
<h2>Can this be a category?</h2>
@ -307,6 +312,16 @@ such that for each \(f:A→B\):</p>
</figure>
</section>
<section class="slide">
<h2>Categories Examples</h2>
<figure style="width:70%; margin:0 auto">
<img src="categories/img/basket_of_cats.jpg" alt="Basket of cats"/>
<figcaption>
<em>- Basket of Cats -</em>
</figcaption>
</figure>
</section>
<section class="slide">
<h2>Category \(\Set\)</h2>
<ul>
@ -323,7 +338,7 @@ such that for each \(f:A→B\):</p>
</section>
<section class="slide">
<h2>Categories Everywhere?</h2>
<img class="right" src="categories/img/cats-everywhere.jpg" alt="Cats everywhere"/>
<ul>
<li>\(\Mon\): (monoids, monoid morphisms,∘)</li>
<li>\(\Vec\): (Vectorial spaces, linear functions,∘)</li>
@ -418,8 +433,8 @@ such that for each \(f:A→B\):</p>
</section>
<section class="slide">
<h2 id="isomorph">Isomorph</h2>
<p><em class="yellow">isomorphism</em>: (f:A→B) which can be &quot;undone&quot; <em>i.e.</em><br />\(∃g:B→A\), \(g∘f=id_A\) <span class="and">&amp;</span> \(f∘g=id_B\)<br />in this case, \(A\) <span class="and">&amp;</span> \(B\) are <em class="yellow">isomorphic</em>.</p>
<p>In Category Theory, <span class="yellow">=</span> is generally <span class="yellow"></span>. For example in commutative diagrams.</p>
<p><img class="right" alt="isomorph cats" src="categories/img/isomorph-cats.jpg" /> <em class="yellow">isomorphism</em>: \(f:A→B\) which can be &quot;undone&quot; <em>i.e.</em><br />\(∃g:B→A\), \(g∘f=id_A\) <span class="and">&amp;</span> \(f∘g=id_B\)<br />in this case, \(A\) <span class="and">&amp;</span> \(B\) are <em class="yellow">isomorphic</em>.</p>
<p><span class="yellow">A≌B</span> means A and B are essentially the same.<br />In Category Theory, <span class="yellow">=</span> is in fact mostly <span class="yellow"></span>.<br />For example in commutative diagrams.</p>
</section>
<section class="slide">
<h2>Functor</h2>
@ -441,28 +456,28 @@ A <em>functor</em> <span class="yellow">\(\F\)</span> from <span class="blue">\(
<section class="slide">
<h2>Functor Example (ob → ob)</h2>
<img width="70%" src="categories/img/mp/functor.png" alt="Functor"/>
<img width="65%" src="categories/img/mp/functor.png" alt="Functor"/>
</section>
<section class="slide">
<h2>Functor Example (hom → hom)</h2>
<img width="70%" src="categories/img/mp/functor-morphism.png" alt="Functor"/>
<img width="65%" src="categories/img/mp/functor-morphism.png" alt="Functor"/>
</section>
<section class="slide">
<h2>Functor Example</h2>
<img width="70%" src="categories/img/mp/functor-morphism-color.png" alt="Functor"/>
<img width="65%" src="categories/img/mp/functor-morphism-color.png" alt="Functor"/>
</section>
<section class="slide">
<h2>Endofunctors</h2>
<p>An <em>endofunctor</em> for \(\C\) is a functor \(F:\C→\C\).</p>
<img src="categories/img/mp/endofunctor.png" alt="Endofunctor"/>
<img width="75%" src="categories/img/mp/endofunctor.png" alt="Endofunctor"/>
</section>
<section class="slide">
<h2>Category of Categories</h2>
<img class="right" src="categories/img/fractalcat.jpg" />
<img style="min-width:43%; width: 43%" class="right" src="categories/img/fractalcat.jpg" />
<p>Categories and functors form a category: \(\Cat\)</p>
<ul><li>\(\ob{\Cat}\) are categories
@ -580,7 +595,7 @@ fmap head [[1,2,3],[4,5,6]] == [1,4]</code></pre>
<p>Put normal function inside a container. Ex: list, trees...<p>
<img src="categories/img/mp/boxfunctor.png" alt="Haskell Functor as a box play"/>
<img width="70%" src="categories/img/mp/boxfunctor.png" alt="Haskell Functor as a box play"/>
</section>
<section class="slide">
<h2>Haskell Functor properties</h2>
@ -597,7 +612,7 @@ fmap head [[1,2,3],[4,5,6]] == [1,4]</code></pre>
<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
Haskell types is fractal:</p>
<img src="categories/img/mp/hask-endofunctor.png" alt="Haskell functor representation"/>
<img width="70%" src="categories/img/mp/hask-endofunctor.png" alt="Haskell functor representation"/>
</section>
<section class="slide">
<h2>Functor as boxes</h2>
@ -605,7 +620,7 @@ Haskell types is fractal:</p>
<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
Haskell types is fractal:</p>
<img src="categories/img/mp/hask-endofunctor-objects.png" alt="Haskell functor representation"/>
<img width="70%" src="categories/img/mp/hask-endofunctor-objects.png" alt="Haskell functor representation"/>
</section>
<section class="slide">
<h2>Functor as boxes</h2>
@ -613,7 +628,7 @@ Haskell types is fractal:</p>
<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
Haskell types is fractal:</p>
<img src="categories/img/mp/hask-endofunctor-morphisms.png" alt="Haskell functor representation"/>
<img width="70%" src="categories/img/mp/hask-endofunctor-morphisms.png" alt="Haskell functor representation"/>
</section>
<section class="slide">
<h2 id="non-haskell-hasks-functors">&quot;Non Haskell&quot; Hask's Functors</h2>
@ -650,7 +665,7 @@ Haskell types is fractal:</p>
</section>
<section class="slide">
<h2 id="category-of-hask-endofunctors">Category of \(\Hask\) Endofunctors</h2>
<img width="70%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
<img width="60%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
</section>
<section class="slide">
<h2 id="category-of-functors">Category of Functors</h2>
@ -882,7 +897,7 @@ drawPoint p = do
</section>
<section class="slide">
<h2 id="fold"><code>fold</code></h2>
<img src="categories/img/tower_folded.gif" alt="fold" style="width:60%;max-width:60%"/>
<img src="categories/img/tower_folded.gif" alt="fold" style="width:50%;max-width:50%"/>
</section>
<section class="slide">
<h2 id="κατα-morphism">κατα-morphism</h2>

View file

@ -1,5 +1,5 @@
<h2 id="general-overview">General Overview</h2>
<div style="float:right; width: 20%">
<div style="float:right; width: 18%">
<img src="categories/img/eilenberg.gif" alt="Samuel Eilenberg"/> <img src="categories/img/maclaine.jpg" alt="Saunders Mac Lane"/>
</div>

View file

@ -1,7 +1,7 @@
General Overview
----------------
<div style="float:right; width: 20%">
<div style="float:right; width: 18%">
<img src="categories/img/eilenberg.gif" alt="Samuel Eilenberg"/>
<img src="categories/img/maclaine.jpg" alt="Saunders Mac Lane"/>
</div>

View file

@ -1,3 +1,8 @@
<h2>Question Time!</h2>
<img width="60%" src="categories/img/batquestion.jpg"/>
<figure style="width:70%; margin:0 auto">
<img src="categories/img/batquestion.jpg" width="100%"/>
<figcaption>
<em>- French-only joke -</em>
</figcaption>
</figure>

View file

@ -0,0 +1,8 @@
<h2>Categories Examples</h2>
<figure style="width:70%; margin:0 auto">
<img src="categories/img/basket_of_cats.jpg" alt="Basket of cats"/>
<figcaption>
<em>- Basket of Cats -</em>
</figcaption>
</figure>

View file

@ -1,5 +1,5 @@
<h2>Categories Everywhere?</h2>
<img class="right" src="categories/img/cats-everywhere.jpg" alt="Cats everywhere"/>
<ul>
<li>\(\Mon\): (monoids, monoid morphisms,∘)</li>
<li>\(\Vec\): (Vectorial spaces, linear functions,∘)</li>

View file

@ -1,3 +1,3 @@
<h2 id="isomorph">Isomorph</h2>
<p><em class="yellow">isomorphism</em>: (f:A→B) which can be &quot;undone&quot; <em>i.e.</em><br />\(∃g:B→A\), \(g∘f=id_A\) &amp; \(f∘g=id_B\)<br />in this case, \(A\) &amp; \(B\) are <em class="yellow">isomorphic</em>.</p>
<p>In Category Theory, <span class="yellow">=</span> is generally <span class="yellow"></span>. For example in commutative diagrams.</p>
<p><img class="right" alt="isomorph cats" src="categories/img/isomorph-cats.jpg" /> <em class="yellow">isomorphism</em>: \(f:A→B\) which can be &quot;undone&quot; <em>i.e.</em><br />\(∃g:B→A\), \(g∘f=id_A\) &amp; \(f∘g=id_B\)<br />in this case, \(A\) &amp; \(B\) are <em class="yellow">isomorphic</em>.</p>
<p><span class="yellow">A≌B</span> means A and B are essentially the same.<br />In Category Theory, <span class="yellow">=</span> is in fact mostly <span class="yellow"></span>.<br />For example in commutative diagrams.</p>

View file

@ -1,9 +1,11 @@
Isomorph
--------
<img class="right" alt="isomorph cats" src="categories/img/isomorph-cats.jpg" />
<em class="yellow">isomorphism</em>:
\(f:A→B\) which can be "undone" _i.e._
\\(f:A→B\\) which can be "undone" _i.e._
\\(∃g:B→A\\), \\(g∘f=id\_A\\) & \\(f∘g=id\_B\\)
in this case, \\(A\\) &amp; \\(B\\) are <em class="yellow">isomorphic</em>.
In Category Theory, <span class="yellow">=</span> is generally <span class="yellow"></span>. For example in commutative diagrams.
<span class="yellow">A≌B</span> means A and B are essentially the same.
In Category Theory, <span class="yellow">=</span> is in fact mostly <span class="yellow"></span>.
For example in commutative diagrams.

View file

@ -1,3 +1,3 @@
<h2>Functor Example (ob → ob)</h2>
<img width="70%" src="categories/img/mp/functor.png" alt="Functor"/>
<img width="65%" src="categories/img/mp/functor.png" alt="Functor"/>

View file

@ -1,3 +1,3 @@
<h2>Functor Example (hom → hom)</h2>
<img width="70%" src="categories/img/mp/functor-morphism.png" alt="Functor"/>
<img width="65%" src="categories/img/mp/functor-morphism.png" alt="Functor"/>

View file

@ -1,3 +1,3 @@
<h2>Functor Example</h2>
<img width="70%" src="categories/img/mp/functor-morphism-color.png" alt="Functor"/>
<img width="65%" src="categories/img/mp/functor-morphism-color.png" alt="Functor"/>

View file

@ -1,4 +1,4 @@
<h2>Endofunctors</h2>
<p>An <em>endofunctor</em> for \(\C\) is a functor \(F:\C→\C\).</p>
<img src="categories/img/mp/endofunctor.png" alt="Endofunctor"/>
<img width="75%" src="categories/img/mp/endofunctor.png" alt="Endofunctor"/>

View file

@ -1,6 +1,6 @@
<h2>Category of Categories</h2>
<img class="right" src="categories/img/fractalcat.jpg" />
<img style="min-width:43%; width: 43%" class="right" src="categories/img/fractalcat.jpg" />
<p>Categories and functors form a category: \(\Cat\)</p>
<ul><li>\(\ob{\Cat}\) are categories

View file

@ -2,4 +2,4 @@
<p>Put normal function inside a container. Ex: list, trees...<p>
<img src="categories/img/mp/boxfunctor.png" alt="Haskell Functor as a box play"/>
<img width="70%" src="categories/img/mp/boxfunctor.png" alt="Haskell Functor as a box play"/>

View file

@ -3,4 +3,4 @@
<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
Haskell types is fractal:</p>
<img src="categories/img/mp/hask-endofunctor.png" alt="Haskell functor representation"/>
<img width="70%" src="categories/img/mp/hask-endofunctor.png" alt="Haskell functor representation"/>

View file

@ -3,4 +3,4 @@
<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
Haskell types is fractal:</p>
<img src="categories/img/mp/hask-endofunctor-objects.png" alt="Haskell functor representation"/>
<img width="70%" src="categories/img/mp/hask-endofunctor-objects.png" alt="Haskell functor representation"/>

View file

@ -3,4 +3,4 @@
<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
Haskell types is fractal:</p>
<img src="categories/img/mp/hask-endofunctor-morphisms.png" alt="Haskell functor representation"/>
<img width="70%" src="categories/img/mp/hask-endofunctor-morphisms.png" alt="Haskell functor representation"/>

View file

@ -1,2 +1,2 @@
<h2 id="category-of-hask-endofunctors">Category of \(\Hask\) Endofunctors</h2>
<img width="70%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
<img width="60%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />

View file

@ -1,4 +1,4 @@
Category of \\(\\Hask\\) Endofunctors
------------------------------------
<img width="70%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
<img width="60%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />

View file

@ -1,2 +1,2 @@
<h2 id="fold"><code>fold</code></h2>
<img src="categories/img/tower_folded.gif" alt="fold" style="width:60%;max-width:60%"/>
<img src="categories/img/tower_folded.gif" alt="fold" style="width:50%;max-width:50%"/>

View file

@ -1,4 +1,4 @@
`fold`
------
<img src="categories/img/tower_folded.gif" alt="fold" style="width:60%;max-width:60%"/>
<img src="categories/img/tower_folded.gif" alt="fold" style="width:50%;max-width:50%"/>

Binary file not shown.

After

Width:  |  Height:  |  Size: 48 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 51 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 2 MiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 33 KiB