Modules

Although the applications of homological algebra that we ultimately aim for are to modules, it is advantageous to work with the wider notion of complexes. Modules are elementary complexes, or complexes are modules with extra structure, depending on the point of view. In any event, there is a decision to make about when to leave modules and pass to complexes. We make this transition as soon as we have established a baseline of homological module theory that allows us to interpret results about complexes in the realm of modules. That baseline is established in this first chapter, and the transition to complexes takes place in Chap. 2.