morel – Konrad Voelkel's Blog – Mathemagically

Is it possible to prove the Quillen-Suslin theorem analogous to the classical theorem on vector bundles over contractible spaces via representing the vectorbundle-up-to-iso-functor in the homotopy category by infinite Grassmannians?

Chapter 2.1. Homotopy theory of simplicial sheaves: The simplicial model category structure. Discussion of 1.2, 1.3, 1.4, 1.5, 1.6, 1.8, 1.9, 1.10.

Background needed to understand Morel-Voevodsky's paper "A¹-homotopy theory". I explain simplicial sets, topoi, monoidal categories, enriched categories and simplicial model categories.

Here is the second part of my walk-through to Morel-Voevodskys A¹-homotopy theory. I give a proof of Lemma 1.1 on page 48.