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It seems to be standard that connective spectra are "the same" as infinite loop space. However, I do not understand the reason why the associated spectrum is connective. For me, an infinite loop ...

My question is both for the topological and for the algebraic/motivic version of the stable homotopy category $\mathbf{SH}$. It is well known that most cohomologies are represented in $\mathbf{SH}$ by ...