ABSTRACT
The quantum groups theory has appeared at the beginning of the years 1980, under the direct influence of some theoretical physics problems. Indeed, V. G. Drinfeld has shown that there is a relationship between solutions of the Yang-Baxter equation and the theory of quantum group representations. The connection between algebra and the Mathematical Physics can be explicated by the formalism of braided monoidal categories. This chapter shows that a braided category is equipped with an associative tensor product and natural isomorphisms. It gives a braided formulation of the homology of a Lie algebra g with coefficients in a g-module M. The chapter also presents definitions from the theory of braided categories. One of the most basic notions of braided category theory, that of algebras.
