An Introduction to Categories and Homological Algebra: A Tale of Four Functors - Ragland, Caedmon (East Carolina University)
We assume familiarity with group theory and discuss the technical background necessary to construct and understand the functors Hom, Ext, T or and tensor on the category of abelian groups, with special attention paid to Hom and Ext. In doing so, we hope to provide an introduction to the study of category theory and homological algebra understandable to an undergraduate with 1-2 semesters of abstract algebra.
Keywords: Extensions; Introduction; Elementary; Category Theory; Group; Groups; Abelian; Ext; Hom; Tensor; Tor; Algebra, Homological; Categories (Mathematics); Group theory; Mathematics--Study and teaching (Higher)