Chain contracting homotopy and a method for relative projective resolutions

Abstract

The purpose of this article is to check the main results of the method that allows the construction of a relative projective resolution of an S-module N given in appendix A of the article [1], and to show an application of this method. It is achieve to show the usefulness of the method, and to put in relevance that the relative projective resolution obtained with the method is comparable to the bar resolution of an algebra because it is provided with chain contracting homotopy.

Keywords

• mapping cone
• homotopy equivalence
• projective class
• contracting homotopy