Constructing Comparison Morphisms Via Weak Slef-homotopies With Applications To Monomial Algebras

The comparison lemma in homological algebra says that two projective resolu-tions of a module are homotopy equivalent and these homotopy equivalences are called comparison morphisms.Sometimes in practice we need the actual construction of these comparison morphisms.The goal of this master thesis is to construct comparison morphisms by using weak self-homotopies.Firstly,we presents the method to construct inductively comparison morphisms between free resolutions,using weak self-homotopy.Then we extend this method to projective resolutions.Finally,we apply this method to monomial algebras;by using Sk(?)lberg’s weak self-homotopy on Bardzell’s resolution,we construct comparison mor-phisms between reduced bar resolution and Bardzell’s resolution,which are different from the comparison morphisms constructed by Roman and Redondo.