Category Theory

Math 531 - Spring 2004


This course is intended for students interested in topology, algebraic geometry, representation theory and other areas that use categorical concepts. I imagine three broad areas which we will study, but how extensively we go into each topic will depend on the interests of the students.

                                                             Relevant texts (Notes will be provided):

MacLane: Category Theory for the working mathematician

Rotman: An Introduction to Homological Algebra

Dwyer and Spalinski: Homotopy theories and model categories

                                                                                        Topics:

1. Basic category theory: examples of categories and functors. The oposite category. Adjoint functors. Products and coproducts, initial and terminal objects, pointed categories. Small categories. Diagrams. Limits and colimits.

2. Additive categories, Abelian categories, resolutions and derived functors (e.g., Ext and  Tor)

3.  Simplicial sets and simplicial objects, classifying spaces of categories, derived categories, model categories.