Mathematics 583

Mathematics 583 Spring 2004

Week 1: introduction, limits and colimits.
Week 2: definition of model category and the associated homotopy category
Week 3: show that the hom sets in the homotopy category are actually sets, by studying the notion of homotopy in the full subcategory of fibrant and cofibrant objects.
Week 4: start working on examples, by studying cofibrantly generated model categories. This involves a bit of set theory.
Week 5: more on cofibrantly generated model categories: the small object argument, and (I hope) some examples, starting with the derived category.
Week 6: the model category structure for topological spaces. Simplicial sets.
Week 7: more on simplicial sets.
Week 8: finish simplicial sets. functors between model categories.
Week 9: homotopy theory in a pointed model category.
Week 10: miscellaneous comments on model categories.

Notes on set theory, in DVI format, in PDF format, or just as a web page (which may not look very good in all web browsers).
errata for the book (DVI file, from Mark Hovey's web page)
course syllabus (on-line)
course syllabus (PDF file)