Abstract.  

Exactness of a sequence of Abelian groups is a wonderful thing – it allows one to extort a great deal of information about the groups (rings, modules, etc) involved. Unfortunately it is not preserved by the Hom(_,D) functor which takes an object and returns all the homomorphisms from that object into a new object D. I intend to explore this “failure of exactness,” covering the ideas of chain complexes, projective resolutions, and the Ext groups. I will be (loosely) following Ch 17 of Dummit & Foote.