Here is the second part of my walk-through to Voevodskys A¹-homotopy theory:

On page 48, the first Lemma is shown. Without proof - so I will try to illuminate things a little bit by giving the proof. This lemma isn't used until section 3, so you can skip it, if you want to. I suggest not to do so, if you are intimidated by the diagram, because it isn't that hard, and it's a nice exercise to get the concepts in your head right.

Continue reading «Walk-through to Morel-Voevodsky A¹-homotopy theory part II (page 48, Lemma 1.1)»

As I'm currently reading Morel&Voevodskys paper on A¹-homotopy theory of schemes, I will by and by write a little "walk-through" with hints & comments on how to find additional information to better (or even start to) understand the paper. Maybe for a newcomer to the subject (like me) it's difficult at first to stick together all these concepts like model theory, simplicial objects, Grothendieck topologies, algebraic geometry and so on. I will try to provide helpful comments to make the paper more accessible to those who are not that familiar with these notions above.

Continue reading «Walk-through to Morel-Voevodsky: A¹-homotopy theory of schemes (1999)»