The parallel constructions of Motivic Homotopy and Motivic Homology are based on the construction of stable homotopy and homology in topology. Instead of starting with topological spaces and using the unit interval [0,1] to define homotopy, one starts with smooth schemes over a fixed field k and uses the affine line A~1 = Spec(k[t]). The constructions are related by two functors from homotopy to homology which, by analogy, we call Hurewicz functors. Here is the main diagram, or road map.
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