fixed sizes
This commit is contained in:
parent
765ff15e95
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25 changed files with 68 additions and 38 deletions
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@ -94,7 +94,7 @@
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</section>
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<section class="slide">
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<h2 id="general-overview">General Overview</h2>
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<div style="float:right; width: 20%">
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<div style="float:right; width: 18%">
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<img src="categories/img/eilenberg.gif" alt="Samuel Eilenberg"/> <img src="categories/img/maclaine.jpg" alt="Saunders Mac Lane"/>
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</div>
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@ -262,7 +262,12 @@ such that for each \(f:A→B\):</p>
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<section class="slide">
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<h2>Question Time!</h2>
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<img width="60%" src="categories/img/batquestion.jpg"/>
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<figure style="width:70%; margin:0 auto">
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<img src="categories/img/batquestion.jpg" width="100%"/>
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<figcaption>
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<em>- French-only joke -</em>
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</figcaption>
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</figure>
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</section>
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<section class="slide">
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<h2>Can this be a category?</h2>
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@ -307,6 +312,16 @@ such that for each \(f:A→B\):</p>
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</figure>
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</section>
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<section class="slide">
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<h2>Categories Examples</h2>
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<figure style="width:70%; margin:0 auto">
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<img src="categories/img/basket_of_cats.jpg" alt="Basket of cats"/>
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<figcaption>
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<em>- Basket of Cats -</em>
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</figcaption>
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</figure>
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</section>
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<section class="slide">
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<h2>Category \(\Set\)</h2>
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<ul>
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@ -323,7 +338,7 @@ such that for each \(f:A→B\):</p>
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</section>
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<section class="slide">
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<h2>Categories Everywhere?</h2>
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<img class="right" src="categories/img/cats-everywhere.jpg" alt="Cats everywhere"/>
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<ul>
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<li>\(\Mon\): (monoids, monoid morphisms,∘)</li>
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<li>\(\Vec\): (Vectorial spaces, linear functions,∘)</li>
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@ -418,8 +433,8 @@ such that for each \(f:A→B\):</p>
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</section>
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<section class="slide">
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<h2 id="isomorph">Isomorph</h2>
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<p><em class="yellow">isomorphism</em>: (f:A→B) which can be "undone" <em>i.e.</em><br />\(∃g:B→A\), \(g∘f=id_A\) <span class="and">&</span> \(f∘g=id_B\)<br />in this case, \(A\) <span class="and">&</span> \(B\) are <em class="yellow">isomorphic</em>.</p>
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<p>In Category Theory, <span class="yellow">=</span> is generally <span class="yellow">≌</span>. For example in commutative diagrams.</p>
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<p><img class="right" alt="isomorph cats" src="categories/img/isomorph-cats.jpg" /> <em class="yellow">isomorphism</em>: \(f:A→B\) which can be "undone" <em>i.e.</em><br />\(∃g:B→A\), \(g∘f=id_A\) <span class="and">&</span> \(f∘g=id_B\)<br />in this case, \(A\) <span class="and">&</span> \(B\) are <em class="yellow">isomorphic</em>.</p>
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<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>
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</section>
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<section class="slide">
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<h2>Functor</h2>
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@ -441,28 +456,28 @@ A <em>functor</em> <span class="yellow">\(\F\)</span> from <span class="blue">\(
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<section class="slide">
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<h2>Functor Example (ob → ob)</h2>
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<img width="70%" src="categories/img/mp/functor.png" alt="Functor"/>
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<img width="65%" src="categories/img/mp/functor.png" alt="Functor"/>
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</section>
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<section class="slide">
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<h2>Functor Example (hom → hom)</h2>
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<img width="70%" src="categories/img/mp/functor-morphism.png" alt="Functor"/>
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<img width="65%" src="categories/img/mp/functor-morphism.png" alt="Functor"/>
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</section>
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<section class="slide">
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<h2>Functor Example</h2>
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<img width="70%" src="categories/img/mp/functor-morphism-color.png" alt="Functor"/>
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<img width="65%" src="categories/img/mp/functor-morphism-color.png" alt="Functor"/>
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</section>
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<section class="slide">
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<h2>Endofunctors</h2>
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<p>An <em>endofunctor</em> for \(\C\) is a functor \(F:\C→\C\).</p>
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<img src="categories/img/mp/endofunctor.png" alt="Endofunctor"/>
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<img width="75%" src="categories/img/mp/endofunctor.png" alt="Endofunctor"/>
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</section>
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<section class="slide">
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<h2>Category of Categories</h2>
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<img class="right" src="categories/img/fractalcat.jpg" />
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<img style="min-width:43%; width: 43%" class="right" src="categories/img/fractalcat.jpg" />
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<p>Categories and functors form a category: \(\Cat\)</p>
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<ul><li>\(\ob{\Cat}\) are categories
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@ -580,7 +595,7 @@ fmap head [[1,2,3],[4,5,6]] == [1,4]</code></pre>
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<p>Put normal function inside a container. Ex: list, trees...<p>
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<img src="categories/img/mp/boxfunctor.png" alt="Haskell Functor as a box play"/>
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<img width="70%" src="categories/img/mp/boxfunctor.png" alt="Haskell Functor as a box play"/>
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</section>
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<section class="slide">
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<h2>Haskell Functor properties</h2>
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@ -597,7 +612,7 @@ fmap head [[1,2,3],[4,5,6]] == [1,4]</code></pre>
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<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
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Haskell types is fractal:</p>
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<img src="categories/img/mp/hask-endofunctor.png" alt="Haskell functor representation"/>
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<img width="70%" src="categories/img/mp/hask-endofunctor.png" alt="Haskell functor representation"/>
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</section>
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<section class="slide">
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<h2>Functor as boxes</h2>
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@ -605,7 +620,7 @@ Haskell types is fractal:</p>
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<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
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Haskell types is fractal:</p>
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<img src="categories/img/mp/hask-endofunctor-objects.png" alt="Haskell functor representation"/>
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<img width="70%" src="categories/img/mp/hask-endofunctor-objects.png" alt="Haskell functor representation"/>
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</section>
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<section class="slide">
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<h2>Functor as boxes</h2>
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@ -613,7 +628,7 @@ Haskell types is fractal:</p>
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<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
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Haskell types is fractal:</p>
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<img src="categories/img/mp/hask-endofunctor-morphisms.png" alt="Haskell functor representation"/>
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<img width="70%" src="categories/img/mp/hask-endofunctor-morphisms.png" alt="Haskell functor representation"/>
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</section>
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<section class="slide">
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<h2 id="non-haskell-hasks-functors">"Non Haskell" Hask's Functors</h2>
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</section>
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<section class="slide">
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<h2 id="category-of-hask-endofunctors">Category of \(\Hask\) Endofunctors</h2>
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<img width="70%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
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<img width="60%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
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</section>
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<section class="slide">
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<h2 id="category-of-functors">Category of Functors</h2>
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@ -882,7 +897,7 @@ drawPoint p = do
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</section>
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<section class="slide">
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<h2 id="fold"><code>fold</code></h2>
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<img src="categories/img/tower_folded.gif" alt="fold" style="width:60%;max-width:60%"/>
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<img src="categories/img/tower_folded.gif" alt="fold" style="width:50%;max-width:50%"/>
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</section>
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<section class="slide">
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<h2 id="κατα-morphism">κατα-morphism</h2>
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@ -1,5 +1,5 @@
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<h2 id="general-overview">General Overview</h2>
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<div style="float:right; width: 20%">
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<div style="float:right; width: 18%">
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<img src="categories/img/eilenberg.gif" alt="Samuel Eilenberg"/> <img src="categories/img/maclaine.jpg" alt="Saunders Mac Lane"/>
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</div>
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@ -1,7 +1,7 @@
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General Overview
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----------------
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<div style="float:right; width: 20%">
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<div style="float:right; width: 18%">
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<img src="categories/img/eilenberg.gif" alt="Samuel Eilenberg"/>
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<img src="categories/img/maclaine.jpg" alt="Saunders Mac Lane"/>
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</div>
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@ -1,3 +1,8 @@
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<h2>Question Time!</h2>
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<img width="60%" src="categories/img/batquestion.jpg"/>
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<figure style="width:70%; margin:0 auto">
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<img src="categories/img/batquestion.jpg" width="100%"/>
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<figcaption>
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<em>- French-only joke -</em>
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</figcaption>
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</figure>
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8
categories/20_What/105.html
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8
categories/20_What/105.html
Normal file
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<h2>Categories Examples</h2>
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<figure style="width:70%; margin:0 auto">
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<img src="categories/img/basket_of_cats.jpg" alt="Basket of cats"/>
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<figcaption>
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<em>- Basket of Cats -</em>
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</figcaption>
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</figure>
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@ -1,5 +1,5 @@
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<h2>Categories Everywhere?</h2>
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<img class="right" src="categories/img/cats-everywhere.jpg" alt="Cats everywhere"/>
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<ul>
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<li>\(\Mon\): (monoids, monoid morphisms,∘)</li>
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<li>\(\Vec\): (Vectorial spaces, linear functions,∘)</li>
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@ -1,3 +1,3 @@
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<h2 id="isomorph">Isomorph</h2>
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<p><em class="yellow">isomorphism</em>: (f:A→B) which can be "undone" <em>i.e.</em><br />\(∃g:B→A\), \(g∘f=id_A\) & \(f∘g=id_B\)<br />in this case, \(A\) & \(B\) are <em class="yellow">isomorphic</em>.</p>
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<p>In Category Theory, <span class="yellow">=</span> is generally <span class="yellow">≌</span>. For example in commutative diagrams.</p>
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<p><img class="right" alt="isomorph cats" src="categories/img/isomorph-cats.jpg" /> <em class="yellow">isomorphism</em>: \(f:A→B\) which can be "undone" <em>i.e.</em><br />\(∃g:B→A\), \(g∘f=id_A\) & \(f∘g=id_B\)<br />in this case, \(A\) & \(B\) are <em class="yellow">isomorphic</em>.</p>
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<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>
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@ -1,9 +1,11 @@
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Isomorph
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--------
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<img class="right" alt="isomorph cats" src="categories/img/isomorph-cats.jpg" />
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<em class="yellow">isomorphism</em>:
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\(f:A→B\) which can be "undone" _i.e._
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\\(f:A→B\\) which can be "undone" _i.e._
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\\(∃g:B→A\\), \\(g∘f=id\_A\\) & \\(f∘g=id\_B\\)
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in this case, \\(A\\) & \\(B\\) are <em class="yellow">isomorphic</em>.
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In Category Theory, <span class="yellow">=</span> is generally <span class="yellow">≌</span>. For example in commutative diagrams.
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<span class="yellow">A≌B</span> means A and B are essentially the same.
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In Category Theory, <span class="yellow">=</span> is in fact mostly <span class="yellow">≌</span>.
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For example in commutative diagrams.
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<h2>Functor Example (ob → ob)</h2>
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<img width="70%" src="categories/img/mp/functor.png" alt="Functor"/>
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<img width="65%" src="categories/img/mp/functor.png" alt="Functor"/>
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@ -1,3 +1,3 @@
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<h2>Functor Example (hom → hom)</h2>
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<img width="70%" src="categories/img/mp/functor-morphism.png" alt="Functor"/>
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<img width="65%" src="categories/img/mp/functor-morphism.png" alt="Functor"/>
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<h2>Functor Example</h2>
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<img width="70%" src="categories/img/mp/functor-morphism-color.png" alt="Functor"/>
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<img width="65%" src="categories/img/mp/functor-morphism-color.png" alt="Functor"/>
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<h2>Endofunctors</h2>
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<p>An <em>endofunctor</em> for \(\C\) is a functor \(F:\C→\C\).</p>
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<img src="categories/img/mp/endofunctor.png" alt="Endofunctor"/>
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<img width="75%" src="categories/img/mp/endofunctor.png" alt="Endofunctor"/>
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<h2>Category of Categories</h2>
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<img class="right" src="categories/img/fractalcat.jpg" />
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<img style="min-width:43%; width: 43%" class="right" src="categories/img/fractalcat.jpg" />
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<p>Categories and functors form a category: \(\Cat\)</p>
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<ul><li>\(\ob{\Cat}\) are categories
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@ -2,4 +2,4 @@
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<p>Put normal function inside a container. Ex: list, trees...<p>
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<img src="categories/img/mp/boxfunctor.png" alt="Haskell Functor as a box play"/>
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<img width="70%" src="categories/img/mp/boxfunctor.png" alt="Haskell Functor as a box play"/>
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<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
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Haskell types is fractal:</p>
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<img src="categories/img/mp/hask-endofunctor.png" alt="Haskell functor representation"/>
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<img width="70%" src="categories/img/mp/hask-endofunctor.png" alt="Haskell functor representation"/>
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<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
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Haskell types is fractal:</p>
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<img src="categories/img/mp/hask-endofunctor-objects.png" alt="Haskell functor representation"/>
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<img width="70%" src="categories/img/mp/hask-endofunctor-objects.png" alt="Haskell functor representation"/>
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<p>Haskell functor can be seen as boxes containing all Haskell types and functions.
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Haskell types is fractal:</p>
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<img src="categories/img/mp/hask-endofunctor-morphisms.png" alt="Haskell functor representation"/>
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<img width="70%" src="categories/img/mp/hask-endofunctor-morphisms.png" alt="Haskell functor representation"/>
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<h2 id="category-of-hask-endofunctors">Category of \(\Hask\) Endofunctors</h2>
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<img width="70%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
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<img width="60%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
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Category of \\(\\Hask\\) Endofunctors
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------------------------------------
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<img width="70%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
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<img width="60%" src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
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<h2 id="fold"><code>fold</code></h2>
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<img src="categories/img/tower_folded.gif" alt="fold" style="width:60%;max-width:60%"/>
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<img src="categories/img/tower_folded.gif" alt="fold" style="width:50%;max-width:50%"/>
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`fold`
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------
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<img src="categories/img/tower_folded.gif" alt="fold" style="width:60%;max-width:60%"/>
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<img src="categories/img/tower_folded.gif" alt="fold" style="width:50%;max-width:50%"/>
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BIN
categories/img/basket_of_cats.jpg
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BIN
categories/img/basket_of_cats.jpg
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After Width: | Height: | Size: 48 KiB |
BIN
categories/img/cats-everywhere.jpg
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categories/img/functor-cat.gif
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categories/img/functor-cat.gif
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BIN
categories/img/isomorph-cats.jpg
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categories/img/isomorph-cats.jpg
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