Homotopy II: Explicit description of the homotopy category of a model category (4/12)

End of Section 1.4: explicit description of the homotopy category of a model category, Whitehead theorem.

Lecture 4/12 of the course Homotopy II given online at the Université de Paris. The goal of this course is to introduce modern homotopy theory, its tools and applications. We will be particularly interested in two examples: chain complexes (see the previous Homology course) and topological spaces. We will present Quillen’s model categories, and we will explain the equivalence between topological spaces and simplicial sets. We will illustrate these methods with rational homotopy theory by showing that multiplicative structures of cochains encodes rational homotopy types of topological spaces.