updated organization

categories.html

@@ -648,20 +648,26 @@ Haskell types is fractal:</p>
 </li></ul>
 </section>
 <section class="slide">
-<h2 id="category-of-endofunctors">Category of Endofunctors</h2>
-<p>All endofunctors of \(\C\) form the category \(\E_\C\) of endofunctors of \(\C\).</p>
-<img src="categories/img/mp/natural-transformation.png" alt="Natural transformation commutative diagram" class="right"/>
-<ul>
-<li>\(\ob{\E_\C}\): endofunctors of \(\C\) ; \(F:\C→\C\)</li>
-<li>\(\hom{\E_\C}\): natural transformations
-<ul>
-<li>η familly \(η_X\in\hom{\C}\) for \(X\in\ob{\C}\) s.t.</li>
-<li>for Haskell functors: <code>F a -&gt; G a</code>.<br />Rearragement functions only.</li>
-</ul></li>
-</ul>
+<h2 id="category-of-hask-endofunctors">Category of \(\Hask\) Endofunctors</h2>
+<img src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />
 </section>
 <section class="slide">
-<h2 id="natural-transformation-examples-13">Natural Transformation Examples (1/3)</h2>
+<h2 id="category-of-functors">Category of Functors</h2>
+<p>If \(\C\) is <em>small</em> (\(\hom{\C}\) is a set). All functors from \(\C\) to some category \(\D\) form the category \(\mathrm{Func}(\C,\D)\).</p>
+<img src="categories/img/mp/natural-transformation.png" alt="Natural transformation commutative diagram" class="right"/>
+<ul>
+<li>\(\ob{\mathrm{Func}(\C,\D)}\): Functors \(F:\C→\D\)</li>
+<li>\(\hom{\mathrm{Func}(\C,\D)}\): <em>natural transformations</em>
+<ul>
+<li>η familly \(η_X\in\hom{\D}\) for \(X\in\ob{\C}\) s.t.</li>
+<li>ex: between Haskel functors; <code>F a -&gt; G a</code><br />Rearragement functions only.</li>
+</ul></li>
+<li>∘: Functor composition</li>
+</ul>
+<p>\(\mathrm{Func}(\C,\C)\) is the category of endofunctors of \(\C\).</p>
+</section>
+<section class="slide">
+<h2 id="natural-transformation-examples-14">Natural Transformation Examples (1/4)</h2>
 <pre><code class="haskell">data Tree a = Empty | Node a [Tree a]
 toTree :: [a] -> Tree a
 toTree [] = Empty
@@ -676,7 +682,7 @@ toTree (x:xs) = Node x [toTree xs]</pre>
 
 </section>
 <section class="slide">
-<h2 id="natural-transformation-examples-23">Natural Transformation Examples (2/3)</h2>
+<h2 id="natural-transformation-examples-24">Natural Transformation Examples (2/4)</h2>
 <pre><code class="haskell">data Tree a = Empty | Node a [Tree a]
 toList :: Tree a -> [a]
 toList Empty = []
@@ -691,17 +697,29 @@ toList (Node x l) = [x] ++ concat (map toList l)</pre>
 
 </section>
 <section class="slide">
-<h2 id="natural-transformation-examples-33">Natural Transformation Examples (3/3)</h2>
-<pre><code class="haskell">
-toMaybe :: [a] -> Maybe a   ;   mToList :: Maybe a -> [a]
-toMaybe [] = Nothing        ;   mToList Nothing = []
-toMaybe (x:xs) = Just x     ;   mToList Just x  = [x]
-</pre>
+<h2 id="natural-transformation-examples-34">Natural Transformation Examples (3/4)</h2>
+<pre><code class="haskell">toMaybe :: [a] -> Maybe a
+toMaybe [] = Nothing
+toMaybe (x:xs) = Just x</pre>
 </code>
 <p><code>toMaybe</code> is a natural transformation. It is also a morphism from <code>[]</code> to <code>Maybe</code> in the Category of \(\) endofunctors.</p>
 <img style="float:left;width:50%" src="categories/img/mp/nattrans-list-maybe.png" alt="natural transformation commutative diagram"/>
 <figure style="float:right;width:40%">
-<img src="categories/img/mp/list-maybe-endofunctor-morphism.png" alt="natural transformation commutative diagram"/> <figcaption>There is <span class="red">no isomorphism</span>.<br/> Hint: <code>Bool</code> lists longer than 1. </figcaption>
+<img src="categories/img/mp/list-maybe-endofunctor-morphism.png" alt="natural transformation commutative diagram"/>
+</figure>
+
+
+</section>
+<section class="slide">
+<h2 id="natural-transformation-examples-44">Natural Transformation Examples (4/4)</h2>
+<pre><code class="haskell">mToList :: Maybe a -> [a]
+mToList Nothing = []
+mToList Just x  = [x]</pre>
+</code>
+<p><code>toMaybe</code> is a natural transformation. It is also a morphism from <code>[]</code> to <code>Maybe</code> in the Category of \(\) endofunctors.</p>
+<img style="float:left;width:50%" src="categories/img/mp/nattrans-maybe-list.png" alt="natural transformation commutative diagram"/>
+<figure style="float:right;width:40%">
+<img src="categories/img/mp/maybe-list-endofunctor-morphsm.png" alt="relation between [] and Maybe"/> <figcaption>There is <span class="red">no isomorphism</span>.<br/> Hint: <code>Bool</code> lists longer than 1. </figcaption>
 </figure>
 
 

categories/30_How/160_Category_of_Endofunctors.html

@@ -1,11 +0,0 @@
-<h2 id="category-of-endofunctors">Category of Endofunctors</h2>
-<p>All endofunctors of \(\C\) form the category \(\E_\C\) of endofunctors of \(\C\).</p>
-<img src="categories/img/mp/natural-transformation.png" alt="Natural transformation commutative diagram" class="right"/>
-<ul>
-<li>\(\ob{\E_\C}\): endofunctors of \(\C\) ; \(F:\C→\C\)</li>
-<li>\(\hom{\E_\C}\): natural transformations
-<ul>
-<li>η familly \(η_X\in\hom{\C}\) for \(X\in\ob{\C}\) s.t.</li>
-<li>for Haskell functors: <code>F a -&gt; G a</code>.<br />Rearragement functions only.</li>
-</ul></li>
-</ul>

categories/30_How/160_Category_of_Endofunctors.md

@@ -1,15 +0,0 @@
-Category of Endofunctors
-------------------------
-
-
-All endofunctors of \\(\\C\\)
-form the category \\(\\E\_\\C\\)
-of endofunctors of \\(\\C\\).
-
-<img src="categories/img/mp/natural-transformation.png" alt="Natural transformation commutative diagram" class="right"/>
-
-- \\(\\ob{\\E\_\\C}\\): endofunctors of \\(\\C\\) ; \\(F:\\C→\\C\\)
-- \\(\\hom{\\E\_\\C}\\): natural transformations
-    - η familly \\(η\_X\\in\\hom{\\C}\\) for \\(X\\in\\ob{\\C}\\) s.t.
-    - for Haskell functors: `F a -> G a`.  
-	Rearragement functions only.

categories/30_How/160_Category_of_Hask_Endofunctors.html

@@ -0,0 +1,2 @@
+<h2 id="category-of-hask-endofunctors">Category of \(\Hask\) Endofunctors</h2>
+<img src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />

categories/30_How/160_Category_of_Hask_Endofunctors.md

@@ -0,0 +1,4 @@
+Category of \\(\\Hask\\) Endofunctors
+------------------------------------
+
+<img src="categories/img/mp/cat-hask-endofunctor.png" alt="Category of Hask endofunctors" />

categories/30_How/170_Category_of_Functors.html

@@ -0,0 +1,13 @@
+<h2 id="category-of-functors">Category of Functors</h2>
+<p>If \(\C\) is <em>small</em> (\(\hom{\C}\) is a set). All functors from \(\C\) to some category \(\D\) form the category \(\mathrm{Func}(\C,\D)\).</p>
+<img src="categories/img/mp/natural-transformation.png" alt="Natural transformation commutative diagram" class="right"/>
+<ul>
+<li>\(\ob{\mathrm{Func}(\C,\D)}\): Functors \(F:\C→\D\)</li>
+<li>\(\hom{\mathrm{Func}(\C,\D)}\): <em>natural transformations</em>
+<ul>
+<li>η familly \(η_X\in\hom{\D}\) for \(X\in\ob{\C}\) s.t.</li>
+<li>ex: between Haskel functors; <code>F a -&gt; G a</code><br />Rearragement functions only.</li>
+</ul></li>
+<li>∘: Functor composition</li>
+</ul>
+<p>\(\mathrm{Func}(\C,\C)\) is the category of endofunctors of \(\C\).</p>

categories/30_How/170_Category_of_Functors.md

@@ -0,0 +1,18 @@
+Category of Functors
+------------------------
+
+If \\(\\C\\) is _small_ (\\(\\hom{\\C}\\) is a set).
+All functors from \\(\\C\\) to some category \\(\\D\\)
+form the category \\(\\mathrm{Func}(\\C,\\D)\\).
+
+<img src="categories/img/mp/natural-transformation.png" alt="Natural transformation commutative diagram" class="right"/>
+
+- \\(\\ob{\\mathrm{Func}(\\C,\\D)}\\): Functors \\(F:\\C→\\D\\)
+- \\(\\hom{\\mathrm{Func}(\\C,\\D)}\\): _natural transformations_
+    - η familly \\(η\_X\\in\\hom{\\D}\\) for \\(X\\in\\ob{\\C}\\) s.t.
+    - ex: between Haskel functors; `F a -> G a`  
+	Rearragement functions only.
+- ∘: Functor composition
+
+
+\\(\\mathrm{Func}(\\C,\\C)\\) is the category of endofunctors of \\(\\C\\).

categories/30_How/180_Natural_Transformation_Examples_1_4.html

@@ -1,4 +1,4 @@
-<h2 id="natural-transformation-examples-13">Natural Transformation Examples (1/3)</h2>
+<h2 id="natural-transformation-examples-14">Natural Transformation Examples (1/4)</h2>
 <pre><code class="haskell">data Tree a = Empty | Node a [Tree a]
 toTree :: [a] -> Tree a
 toTree [] = Empty

categories/30_How/180_Natural_Transformation_Examples_1_4.md

@@ -1,4 +1,4 @@
-Natural Transformation Examples (1/3)
+Natural Transformation Examples (1/4)
 ------------------------------------
 
 <pre><code class="haskell">data Tree a = Empty | Node a [Tree a]

categories/30_How/190_Another_Nat_Trans_Example.html

@@ -1,14 +0,0 @@
-<h2 id="natural-transformation-examples-33">Natural Transformation Examples (3/3)</h2>
-<pre><code class="haskell">
-toMaybe :: [a] -> Maybe a   ;   mToList :: Maybe a -> [a]
-toMaybe [] = Nothing        ;   mToList Nothing = []
-toMaybe (x:xs) = Just x     ;   mToList Just x  = [x]
-</pre>
-</code>
-<p><code>toMaybe</code> is a natural transformation. It is also a morphism from <code>[]</code> to <code>Maybe</code> in the Category of \(\) endofunctors.</p>
-<img style="float:left;width:50%" src="categories/img/mp/nattrans-list-maybe.png" alt="natural transformation commutative diagram"/>
-<figure style="float:right;width:40%">
-<img src="categories/img/mp/list-maybe-endofunctor-morphism.png" alt="natural transformation commutative diagram"/> <figcaption>There is <span class="red">no isomorphism</span>.<br/> Hint: <code>Bool</code> lists longer than 1. </figcaption>
-</figure>
-
-

categories/30_How/190_Natural_Transformation_Examples_2_4.html

@@ -1,4 +1,4 @@
-<h2 id="natural-transformation-examples-23">Natural Transformation Examples (2/3)</h2>
+<h2 id="natural-transformation-examples-24">Natural Transformation Examples (2/4)</h2>
 <pre><code class="haskell">data Tree a = Empty | Node a [Tree a]
 toList :: Tree a -> [a]
 toList Empty = []

categories/30_How/190_Natural_Transformation_Examples_2_4.md

@@ -1,4 +1,4 @@
-Natural Transformation Examples (2/3)
+Natural Transformation Examples (2/4)
 ------------------------------------
 
 <pre><code class="haskell">data Tree a = Empty | Node a [Tree a]

categories/30_How/200_Natural_Transformation_Examples_3_4.html

@@ -0,0 +1,12 @@
+<h2 id="natural-transformation-examples-34">Natural Transformation Examples (3/4)</h2>
+<pre><code class="haskell">toMaybe :: [a] -> Maybe a
+toMaybe [] = Nothing
+toMaybe (x:xs) = Just x</pre>
+</code>
+<p><code>toMaybe</code> is a natural transformation. It is also a morphism from <code>[]</code> to <code>Maybe</code> in the Category of \(\) endofunctors.</p>
+<img style="float:left;width:50%" src="categories/img/mp/nattrans-list-maybe.png" alt="natural transformation commutative diagram"/>
+<figure style="float:right;width:40%">
+<img src="categories/img/mp/list-maybe-endofunctor-morphism.png" alt="natural transformation commutative diagram"/>
+</figure>
+
+

categories/30_How/200_Natural_Transformation_Examples_3_4.md

@@ -1,11 +1,9 @@
-Natural Transformation Examples (3/3)
+Natural Transformation Examples (3/4)
 -------------------------------------
 
-<pre><code class="haskell">
-toMaybe :: [a] -> Maybe a   ;   mToList :: Maybe a -> [a]
-toMaybe [] = Nothing        ;   mToList Nothing = []
-toMaybe (x:xs) = Just x     ;   mToList Just x  = [x]
-</pre></code>
+<pre><code class="haskell">toMaybe :: [a] -> Maybe a
+toMaybe [] = Nothing
+toMaybe (x:xs) = Just x</pre></code>
 
 
 `toMaybe` is a natural transformation.
@@ -14,7 +12,4 @@ It is also a morphism from `[]` to `Maybe` in the Category of \\(\Hask\\) endofu
 <img style="float:left;width:50%" src="categories/img/mp/nattrans-list-maybe.png" alt="natural transformation commutative diagram"/>
 <figure style="float:right;width:40%">
 <img src="categories/img/mp/list-maybe-endofunctor-morphism.png" alt="natural transformation commutative diagram"/>
-<figcaption>There is <span class="red">no isomorphism</span>.<br/>
-Hint: <code>Bool</code> lists longer than 1.
-</figcaption>
 </figure>

categories/30_How/210_Natural_Transformation_Examples_4_4.html

@@ -0,0 +1,12 @@
+<h2 id="natural-transformation-examples-44">Natural Transformation Examples (4/4)</h2>
+<pre><code class="haskell">mToList :: Maybe a -> [a]
+mToList Nothing = []
+mToList Just x  = [x]</pre>
+</code>
+<p><code>toMaybe</code> is a natural transformation. It is also a morphism from <code>[]</code> to <code>Maybe</code> in the Category of \(\) endofunctors.</p>
+<img style="float:left;width:50%" src="categories/img/mp/nattrans-maybe-list.png" alt="natural transformation commutative diagram"/>
+<figure style="float:right;width:40%">
+<img src="categories/img/mp/maybe-list-endofunctor-morphsm.png" alt="relation between [] and Maybe"/> <figcaption>There is <span class="red">no isomorphism</span>.<br/> Hint: <code>Bool</code> lists longer than 1. </figcaption>
+</figure>
+
+

categories/30_How/210_Natural_Transformation_Examples_4_4.md

@@ -0,0 +1,18 @@
+Natural Transformation Examples (4/4)
+-------------------------------------
+
+<pre><code class="haskell">mToList :: Maybe a -> [a]
+mToList Nothing = []
+mToList Just x  = [x]</pre></code>
+
+
+`toMaybe` is a natural transformation.
+It is also a morphism from `[]` to `Maybe` in the Category of \\(\Hask\\) endofunctors.
+
+<img style="float:left;width:50%" src="categories/img/mp/nattrans-maybe-list.png" alt="natural transformation commutative diagram"/>
+<figure style="float:right;width:40%">
+<img src="categories/img/mp/maybe-list-endofunctor-morphsm.png" alt="relation between [] and Maybe"/>
+<figcaption>There is <span class="red">no isomorphism</span>.<br/>
+Hint: <code>Bool</code> lists longer than 1.
+</figcaption>
+</figure>

categories/img/mp/cat-hask-endofunctor.mp

@@ -0,0 +1,108 @@
+% DPI 180
+pair int,bool,func,intlist,list;
+resize(.8cm);
+int=origin;
+% drawoptions (withcolor baseOne withpen pencircle scaled 1.2);
+
+intlist=int shifted (gu,0);
+func=int shifted (0,-.6gu);
+bool=func shifted (gu,0);
+list=func shifted (2u,0);
+
+
+drawLoopPoint(int,int shifted (0,1.6u),"\mathtt{sqrt}");
+drawEdge(int,int,"\mathtt{id}");
+drawEdgeAngle(int,bool,"\mathtt{odd}",-30);
+drawEdgeAngle(int,bool,"\mathtt{even}",30);
+drawEdge(intlist,intlist,"\mathtt{tail}");
+drawEdge(intlist,int,"\mathtt{length}");
+
+% ---------- F ----------------
+
+pair decal;
+pair fint,fbool,ffunc,fintlist,flist;
+decal := (-1.2gu,-1.5gu);
+fint=int shifted decal;
+fintlist=intlist shifted decal;
+ffunc=   func shifted decal;
+fbool=   bool shifted decal;
+flist=   list shifted decal;
+
+drawLoopPoint(fint,fint shifted (0,1.9u),"\scriptstyle\mathtt{fmap\ sqrt}");
+drawEdge(fint,fint,"\scriptstyle\mathtt{fmap\ id}");
+drawEdgeAngle(fint,fbool,"\scriptstyle\mathtt{fmap\ odd}",-30);
+drawEdgeAngle(fint,fbool,"\scriptstyle\mathtt{fmap\ even}",30);
+drawEdge(fintlist,fintlist,"\scriptstyle\mathtt{fmap\ tail}");
+drawEdge(fintlist,fint,"\scriptstyle\mathtt{fmap\ length}");
+
+drawblock(fint,fbool,"\mathtt{F}");
+
+pair ff;
+ff = .5[fint,fintlist] shifted (0,u);
+path b;
+b := block(origin,origin);
+draw b scaled .5 shifted ff;
+label.top(btex $\mathtt{F\ F}$ etex, blockLabelPosition(b)) scaled .5 shifted ff;
+draw b scaled .25 shifted ff;
+label.top(btex $\mathtt{F\ F\ F}$ etex, blockLabelPosition(b)) scaled .25 shifted ff;
+
+% ------------ G --------------
+pair gdecal;
+pair gint,gbool,gfunc,gintlist,glist;
+gdecal := (1.2gu,-1.5gu);
+gint=int shifted gdecal;
+gintlist=intlist shifted gdecal;
+gfunc=   func shifted gdecal;
+gbool=   bool shifted gdecal;
+glist=   list shifted gdecal;
+
+drawLoopPoint(gint,gint shifted (0,1.9u),"\scriptstyle\mathtt{fmap\ sqrt}");
+drawEdge(gint,gint,"\scriptstyle\mathtt{fmap\ id}");
+drawEdgeAngle(gint,gbool,"\scriptstyle\mathtt{fmap\ odd}",-30);
+drawEdgeAngle(gint,gbool,"\scriptstyle\mathtt{fmap\ even}",30);
+drawEdge(gintlist,gintlist,"\scriptstyle\mathtt{fmap\ tail}");
+drawEdge(gintlist,gint,"\scriptstyle\mathtt{fmap\ length}");
+
+drawblock(gint,gbool,"\mathtt{G}");
+
+pair gf;
+gf = .5[gint,gintlist] shifted (0,u);
+path b;
+b := block(origin,origin);
+draw b scaled .5 shifted gf;
+label.top(btex $\mathtt{G\ G}$ etex, blockLabelPosition(b)) scaled .5 shifted gf;
+draw b scaled .25 shifted gf;
+label.top(btex $\mathtt{G\ G\ G}$ etex, blockLabelPosition(b)) scaled .25 shifted gf;
+
+
+drawState(int,"\mathtt{Int}");
+drawState(intlist,"\mathtt{[Int]}");
+drawState(func,"\mathtt{a\rightarrow b}");
+drawState(list,"\mathtt{[a]}");
+drawState(bool,"\mathtt{Bool}");
+
+drawState(fint,"\mathtt{F\ Int}");
+drawState(fintlist,"\mathtt{F\ [Int]}");
+drawState(ffunc,"\mathtt{F\ a\rightarrow b}");
+drawState(flist,"\mathtt{F\ [a]}");
+drawState(fbool,"\mathtt{F\ Bool}");
+
+drawState(gint,"\mathtt{G\ Int}");
+drawState(gintlist,"\mathtt{G\ [Int]}");
+drawState(gfunc,"\mathtt{G\ a\rightarrow b}");
+drawState(glist,"\mathtt{G\ [a]}");
+drawState(gbool,"\mathtt{G\ Bool}");
+
+drawoptions(withcolor yellow);
+label.top(btex $I$ etex, .5[int,intlist] shifted (0,u));
+
+drawoptions(withpen pencircle scaled 2bp withcolor yellow);
+ahlength:=.3u;
+
+drawEdgeAngle(.5[int,func] shifted (-.5u,0), ff shifted (0,2.2u), "?", -30);
+drawEdgeAngle(ff shifted (-u,2.2u), .5[int,func] shifted (-.5u,u), "?", 30);
+drawEdgeAngle(.5[intlist,bool] shifted (.5u,0), gf shifted (0,2.2u), "?", 30);
+drawEdgeAngle(gf shifted (u,2.2u), .5[intlist,bool] shifted (.5u,u), "?", -30);
+
+drawEdgeAngle(.5[fintlist,fbool] shifted (1.1u,u), .5[gint,gfunc] shifted (-1.1u,u), "?", 30);
+drawEdgeAngle(.5[gint,gfunc] shifted (-1.1u,u), .5[fintlist,fbool] shifted (1.1u,u), "?", 30);

categories/img/mp/gen

@@ -64,9 +64,15 @@ for fpfic in $listfic; do
       | sed 's/green/s_green/g' > $tmp
     [[ -e $old ]] && diff $tmp $old >/dev/null && { echo " identical"; continue }
 
-    print -- "[$PWD]: mpost $tmp && convert -density 300 $tmp.1 $png"
+	dpi=$(grep '% DPI' $tmp | awk '{print $3}')
+	[[ $dpi = "" ]] && dpi=600
+
+	print
+	print "[DPI]: $dpi"
+
+    print -- "[$PWD]: mpost $tmp && convert -density $dpi $tmp.1 $png"
     mpost --tex=latex $tmp && \
-		convert -colorspace rgb -density 600 $eps '(' +clone -background black -shadow 90x4+0+1 ')' +swap -background none -layers merge +repage $png && \
+		convert -colorspace rgb -density $dpi $eps '(' +clone -background black -shadow 90x4+0+1 ')' +swap -background none -layers merge +repage $png && \
         \cp -f $png $scriptdir && \
         \cp -f $tmp $old && \
         echo "updated"

categories/img/mp/list-maybe-endofunctor-morphism.mp

@@ -1,8 +1,8 @@
 pair tree,list;
 resize(.8cm);
+
 list=origin;
 tree=list shifted (gu,0);
 drawState(list,"\mathtt{[]}");
 drawState(tree,"\mathtt{Maybe}");
 drawEdgeAngle(list,tree,"\mathtt{toMaybe}",30);
-drawEdgeAngle(tree,list,"\mathtt{mToList}",30);

categories/img/mp/maybe-list-endofunctor-morphsm.mp

@@ -0,0 +1,9 @@
+pair tree,list;
+resize(.8cm);
+list=origin;
+
+tree=list shifted (gu,0);
+drawState(list,"\mathtt{[]}");
+drawState(tree,"\mathtt{Maybe}");
+drawEdgeAngle(list,tree,"\mathtt{toMaybe}",30);
+drawEdgeAngle(tree,list,"\mathtt{mToList}",30);

categories/img/mp/nattrans-list-maybe.mp

@@ -18,11 +18,3 @@ label.lft(btex $\mathtt{toMaybe}$ etex,midpoint(ab));
 ac:=edge(z1,z3);
 drawarrow ac;
 label.rt(btex $\mathtt{toMaybe}$ etex,midpoint(ac));
-
-path abb,acb;
-abb:=edge(z2 shifted (.2u,0),z0 shifted (.2u,0));
-acb:=edge(z3 shifted (-.2u,0),z1 shifted (-.2u,0));
-drawarrow abb;
-drawarrow acb;
-label.rt(btex $\mathtt{mToList}$ etex,midpoint(abb));
-label.lft(btex $\mathtt{mToList}$ etex,midpoint(acb));

categories/img/mp/nattrans-maybe-list.mp

@@ -0,0 +1,21 @@
+z0=(0,0);
+z1=(1.5gu,0);
+z2=(0,-gu);
+z3=(1.5gu,-gu);
+path ac,ab;
+
+label(btex $\mathtt{[a]}$ etex,z0);
+label(btex $\mathtt{[b]}$ etex,z1);
+label(btex $\mathtt{Maybe\ a}$ etex,z2 shifted (-u,0));
+label(btex $\mathtt{Maybe\ b}$ etex,z3 shifted (u,0));
+
+drawEdge(z0,z1,"\mathtt{fmap_{[]}\ f}");
+drawEdge(z2,z3,"\mathtt{fmap_{Maybe}\ f}");
+
+path abb,acb;
+abb:=edge(z2 shifted (.2u,0),z0 shifted (.2u,0));
+acb:=edge(z3 shifted (-.2u,0),z1 shifted (-.2u,0));
+drawarrow abb;
+drawarrow acb;
+label.rt(btex $\mathtt{mToList}$ etex,midpoint(abb));
+label.lft(btex $\mathtt{mToList}$ etex,midpoint(acb));