Topology Seminar

In classical homotopy theory, one can look at continuous maps up to homotopy and consider two topological spaces as essentially the same if they are homotopy equivalent. Model categories, introduced by Quillen, allow us to make similar homotopical constructions in a much broader context. I will present the definition of model category and some basic properties. We will look at the examples of topological spaces, chain complexes, and simplicial sets.