Homological Functors with Coefficients

Abstract

In this thesis, a framework is provided for defining homological functors with coefficients that can be applied to many examples including the usual homotopy and homology functors from algebraic topology, and the K-theory functors. Functors with coefficients in a column-finite matrix of nonnegative integers is first defined, followed by functors with coefficients in an abelian group. From our definition we can obtain a universal coefficient theorem. Categories with a symmetric tensor product structure are also considered.