Serre homotopy theory in subcategories of simplicial sets

ABSTRACTThe thesis consists of two chapters.In the first chapter, the notions of simplicial sets and topological spaces, simplicialobjects and maps, topological standart simplex are described in the early sections. However thenotions and definitions that will be used in the other chapter, are also expressed. The rest of thischapter the closed model categories are shortly described.S⊆» is a multiplicative system and C is the class of the S-In the second chapter, iftorsion abelian sets, we study Serre mod -C homotopy theory in the subcategories of simplicialr and greater than n forsets whose objects have trivial Moore in dimensions less than0 ≤ r ≤ n. This is carried by giving a closed model structure in these categories and thenn→∞, we obtain the Serre homotopy theorystudying the associated homotopy theory. Whenr -reduced simplicial sets studied by Quillen in [6]. The case n=r+1 allows to consider Serreforhomotopy theory in categories of cat-sets or crossed modules of sets.