Stable A1-homotopy Theory
نویسنده
چکیده
Definition 1. A T -prespectrum E is a sequence En of pointed spaces together with structure morphisms σn : En ∧ T → En+1 for all n. A morphism λ : E → F of T -prespectra is a sequence of maps λn : En → Fn commuting with the structure morphisms. We will denote the category of T -prespectra by PSpT (k). Example 1. For any based space X , we have the suspension prespectrum Σ∞(X ) of X given by Σ∞(X )n = X ∧T (n). The structure morphisms are simply the association isomorphisms. Let p, q ∈ Z. For any E ∈ PSpT (k) and U ∈ Smk, we define the stable homotopy group of degree p and weight q to be the presheaf of groups given on some U ∈ Smk by πp,q(E)(U) = colim r [Sp−q+r s ∧G m ∧ (U+), En].
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