Homotopy theory for truncated weak equivalences of simplicial algebras

ABSTRACTThis thesis consists of six chapters.In the preface chapter, the study at the whole thesis is presented shortly.In the first chapter, basic definitions and theories that will be used in the other chaptersare stated, and mentioned about simplicial objects and maps, k-algebras, simplicial algebras,truncated simplicial algebras and free simplicial algebras with CW-komplexes.In the second chapter, homotopy theory for Quillen structure of simplicial algebras,some results for simlicial algebras are examined and definitions of peculiarities of hyperalgebrasare given with examples.In the third chapter, Quillen model structures for algebraic models of r-connectedspaces are given with the theories.In the fourth chapter, model structure for n-type of simplicial algebras is expressed withthe theories.In the fifth chapter, Quillen model structure for (r,n)-types of simplicial algebras isexamined by associating r and n types which are expressed in the third and fourth chapters.