diff --git a/contents/category_theory.tex b/contents/category_theory.tex
index 6615094..f1a2aa9 100644
--- a/contents/category_theory.tex
+++ b/contents/category_theory.tex
@@ -1,9 +1,27 @@
 \langchapter{Théorie des Catégories}{Category theory}
 %TODO Complete chapter
 
+Category is a general theory of mathematical structures and their relations.
+
+\langsection{Définition}{Definition}
+
+A category $C$ is a collection of objects and morphisms
+
 \langsection{Morphismes}{Morphisms}
 %TODO Complete section
 
+\langsubsection{Isomorphisme}{Isomorphism} \label{definition:isomorphism}
+%TODO Complete section
+
+\langsubsection{Endomorphisme}{Endomorphism} \label{definition:endomorphism}
+%TODO Complete section
+
+\langsubsection{Homomorphisme}{Homomorphism}
+%TODO Complete section
+
+\langsubsection{Homeomorphisme}{Homeomorphism}
+%TODO Complete section
+
 \section{Functors}
 %TODO Complete section