Cours fondamental 1 (TA)
Contact : najib.idrissi-kaitouni à imj-prg.fr
Des notes de cours seront disponibles.
The goal of this lecture is to present two ``concrete'' homotopy theories. We will start with the classical homotopy theory of topological spaces (homotopy groups, cellular complexes, Whitehead and Hurewicz theorems, fibrations). Then we will move to the homotopy theory of simplicial sets (definitions, simplex category, adjunction and cosimplicial objects, examples, fibrations, Kan complexes, and simplicial homotopy). The notion of a simplicial set will be introduced with a view toward a definition of infinity-categories.