On homotopy class of quadratic module morphism

This thesis consists of five chapters. In the first chapter, we give some basic information to use in next sections. In the second chapter, we mention crossed modules over commutative algebras and Nil(n)-modules of algebras. In the third chapter, we recall some categorical properties of quadratic modules of algebras and their morphisms. In section 4, we obtain simplexes from quadratic module morphisms. In the last chapter, we give an introduction to the notion of homotopy between the morphisms of quadratic modules.