Categories and Modules with K-Theory in View (Cambridge Studies in Advanced Mathematics)

This book develops aspects of category theory fundamental to the study of algebraic K-theory. Starting with categories in general, the text then examines categories of K-theory and moves on to tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits. The authors consider local-global techniques that supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry. Many useful exercises, concrete illustrations of abstract concepts, and an extensive list of references are included.