Introduction to stable homotopy theory - Lecture 8

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Homotopy groups of spectra, mapping spectra and tensor product
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It seems that the Whitehead theorem says that the category Sp is generated by the spectrum S, is it correct? If this is the case, can this fact be proved directly?

Yuki-dwdn
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Does one have HA⊗HB = H(A⊗B) ? In other word is the embedding of abelian groups in spectra monoidal ?

Varzmir