diff --git a/00_Introduction.lhs b/00_Introduction.lhs
index 0561ea8..954e581 100644
--- a/00_Introduction.lhs
+++ b/00_Introduction.lhs
@@ -1,6 +1,6 @@
  ## Introduction
 
-My last two post where about Haskell and how to do something useful with it.
+%TODO{Do everything after the end}
 
 Now, it is time to talk about Categories.
 How this notion could help you and how it is easy to use with Haskell.
@@ -8,20 +8,21 @@ How this notion could help you and how it is easy to use with Haskell.
 - What are categories?
 - How to use them?
 
-First, a realisation.
+ ### Programming Paradigms
 
-Programming paradigm. When you program, you resolve problems.
+When you program, you resolve problems.
 There are a lot of different means to resolve a problem.
-Some general school of thought exists.
+Many different "school of thought"[^school] exists.
 
+[^school]: Écoles de pensées
+
+**Imperative paradigm**:
 In programming, most people use the imperative paradigm.
-You use some memory and update it.
-More precisely, you destroy part of information by setting variables to new values.
-Hidden somewhere, there is the model of the Turing machine.
-Of course, it is more complex with modern architecture, but the paradigm is the same.
 You have an infinite number of cell and you can write things on them.
-But you must erase them.
+Of course, it is more complex with modern architecture, but the paradigm is the same.
+Hidden somewhere, there is the model of the Turing machine.
 
+**Functional paradigm**:
 Another paradigm, is the functional paradigm.
 This time, you don't write on cells, but instead you have a flow of data.
 And you transform the flows in another flows... Mostly it looks like pipes.
@@ -29,9 +30,9 @@ I am a bit restrictive here. But generally this is how functional programming is
 The main theory behind this paradigm is the Set theory.
 You have a set and you go from one set to another set by using a function.
 
-But using I believe there is another paradigm arising from Category theory.
-And from what I saw up until there.
-Category theory is both more general and powerful to help solve problems.
+**Category paradigm**:
+I believe there is another paradigm arising from Category theory.
+Category theory feels both more general and powerful to help solve problems.
 
 First, you must realize there are categories everywhere.
 With the category theory you can find relationships between quantum physics,
@@ -47,13 +48,17 @@ A paradigm with gates between many different domains.
 We write down the definition first.
 And will discuss about some categories.
 
+<div style="display:none">
+\\( \newcommand{\hom}{\mathrm{hom}} \\)
+</div>
+
  > **Definition**:
  >
  > A category \\(C\\) consist of:
  >
  > - A collection of _objects_ \\(ob(C)\\)
- > - For every pair of objects \\((A,B)\\) a set \\(hom(A,B)\\)
- >   of _morphisms_ \\(f:A→B\\) (Another notation for \\(f\in hom(A,B)\\))
+ > - For every pair of objects \\((A,B)\\) a set \\(\hom(A,B)\\)
+ >   of _morphisms_ \\(f:A→B\\) (Another notation for \\(f\in \hom(A,B)\\))
  > - A composition operator \\(∘\\)
  >   which associate to each couple \\(g:A→B\\), \\(f:B→C\\) another morphism \\(f∘g:A→C\\).
  >
@@ -66,3 +71,114 @@ And will discuss about some categories.
  > - for all triplet of morphisms \\(h:A->B\\), \\(g:B->C\\) and \\(f:C->D\\)  
  >   \\( (f∘g)∘h = f∘(g∘h) \\)
 
+ ### Representation of Category
+
+Representing Category is not just a game.
+It will be _very_ important.
+But in the same time, it will help you to gain intuition about categories.
+
+A naïve representation (which can work in many cases) is to represent
+a specific category as a directed graph.
+Here is a first example of the representation of a category:
+
+<graph title="First Naïve Category Representation">
+
+A -> B [label="f"]
+B -> C [label="g"]
+A -> C [label="h"]
+
+A -> A [label="idA"]
+B -> B [label="idB"]
+C -> C [label="idC"]
+
+</graph>
+
+From this graph we can conclude without any ambiguity that:
+
+\\[ob(C)={A,B,C}\\]
+and
+\\[\hom(C)=\\{f,g,h,idA,idB,idC\\}\\]
+
+Instantaneously, we understand that we can get rid of all \\(idX\\) arrows.
+
+But in reality, we lack an important information.
+What is \\(∘\\)?
+
+Now, we can add informations to our previous representation.
+We simply add a relation between 3 arrows that represent the composition.
+
+<graph title="Naïve Category Representation">
+
+f[label="", fixedsize="false", width=0,height=0,shape=none];
+A -> f[label="f", arrowhead=None]
+f -> B
+
+g[label="", fixedsize="false", width=0,height=0,shape=none];
+B -> g[label="g", arrowhead=None]
+g -> C
+
+fg[label="", fixedsize="false", width=0,height=0,shape=none];
+AC[label="", fixedsize="false", width=0,height=0,shape=none];
+
+f -> fg [style=dashed,arrowhead=None]
+fg -> g [style=dashed,arrowhead=None]
+A -> AC [label="g∘f",arrowhead=None]
+AC -> C
+
+fg -> AC [style=bold]
+
+</graph>
+
+On this little graph things are already complex.
+Let just double the morphisms between different objects.
+
+<graph title="Naïve Category Representation Mess">
+
+f[label="", fixedsize="false", width=0,height=0,shape=none];
+A -> f[label="f", arrowhead=None]
+f -> B
+
+fp[label="", fixedsize="false", width=0,height=0,shape=none];
+A -> fp[label="f'", arrowhead=None]
+fp -> B
+
+g[label="", fixedsize="false", width=0,height=0,shape=none];
+B -> g[label="g", arrowhead=None]
+g -> C
+
+gp[label="", fixedsize="false", width=0,height=0,shape=none];
+B -> gp[label="g'", arrowhead=None]
+gp -> C
+
+fg[label="", fixedsize="false", width=0,height=0,shape=none];
+fpg[label="", fixedsize="false", width=0,height=0,shape=none];
+fgp[label="", fixedsize="false", width=0,height=0,shape=none];
+fpgp[label="", fixedsize="false", width=0,height=0,shape=none];
+
+AC[label="", fixedsize="false", width=0,height=0,shape=none];
+ApCp[label="", fixedsize="false", width=0,height=0,shape=none];
+
+f -> fg [style=dashed,arrowhead=None]
+fg -> g [style=dashed,arrowhead=None]
+
+fp -> fpg [style=dashed,arrowhead=None]
+fpg -> g [style=dashed,arrowhead=None]
+
+f -> fgp [style=dashed,arrowhead=None]
+fgp -> gp [style=dashed,arrowhead=None]
+
+fp -> fpgp [style=dashed,arrowhead=None]
+fpgp -> gp [style=dashed,arrowhead=None]
+
+A -> AC [label="h=g∘f=g'∘f'",arrowhead=None]
+AC -> C
+
+A -> ApCp [label="h'=g'∘f=g∘f'",arrowhead=None]
+ApCp -> C
+
+fg -> AC [style=bold]
+fpgp -> AC [style=bold]
+fpg -> ApCp [style=bold]
+fgp -> ApCp [style=bold]
+
+</graph>