Infinite dimensional manifolds from a new point of view

In this paper we propose a new treatment about infinite dimensional manifolds, using the language of categories and functors. Our definition of infinite dimensional manifolds is a natural generalization of finite dimensional manifolds in the sense that de Rham cohomology and singular cohomology can be naturally defined and the basic properties (Functorial Property, Homotopy Invariant, Mayer-Vietoris Sequence) are preserved. In this setting we define the classifying space BG of a Lie group G as an infinite dimensional manifold. Using simplicial homotopy theory and the Chern-Weil theory for principal G-bundles we show that de Rhamʼs theorem holds for BG when G is compact. Finally we get, as an unexpected byproduct, two simplicial set models for the classifying spaces of compact Lie groups; they are totally different from the classical models constructed by Milnor, Milgram, Segal and Steenrod.