Wednesday, November 14th, 2012 | Author: Konrad Voelkel
We will investigate the notion of cellular objects in a model category; today: the classical case of CW-complexes in the model category of topological spaces with Serre-fibrations as fibrations.
A CW complex is a certain kind of topological space, together with a CW structure, which is a description how to glue the space from spheres (or from affine spaces, if you prefer), called the cells. The acronym CW stands for "closure finite, weak topology", which I will explain soon. CW complexes are a class of spaces broader than simplicial complexes, and they are still combinatorial in nature.