Simplicial presheaves

This thesis gives very deep and large survey about the notions of simplex, complex, the category of simplicial sets and simplicial presheaves which are very important area in the algebraic topology. It is divided into three chapters. The first chapter contains the notions of simplex and complex with the some properties of them. The second chapter devoted to category of simplicial sets, the simplicial fibration and the homotopies among the objects in the category of simplicial sets. It also includes the costruction of the homotopy groups. In the third chapter the Grothendieck 's topology and the notion of site are introduced and the notion of simplicial presheaves is given in this notion of site. Besides, the category of the fibrant objects has been constructed for the category of simplicial presheaves and the homotopy theory this category. Science Code : 403. 04. 01 Key Words : Simplicial sets, Simplicial presheaves, Simplicial fibration