Myles Tierney, Rutgers University

Overview of simplicial homotopy theory

1. The simplicial category, simplicial sets, examples, skeleton, coskeleton, geometric realization, the fundamental category.
2. Retracts, transfinite composition, saturated classes, weak factorisation systems, examples, Quillen model structures, examples.
3. Model structures continued, the homotopy category, Quillen functors and equivalences.
4. Some simplicial homotopy theory, Kan complexes, bundles, cartesian model categories, homotopy.
5. Minimal fibrations, various results, weak equivalences, a sketch of the model structure.
6. The category of pointed simplicial sets, the fundamental groupoid, homotopy groups, Eckmann-Hilton.
7. The long exact sequence, Whitehead's Theorem, Milnor's Theorem, the equivalence of homotopy categories.