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Let $ R$ be a cofibrant commutative $ S$ -algebra (in the sense of Elmendorf-Kriz-Mandell-May; they call them “$ q$ -cofibrant”) and $ A$ be a cofibrant commutative $ R$ -algebra. Does $ A\wedge_R-:RMod→RMod$ preserve all weak equivalences? This could be rephrased as “$ A$ is a flat $ R$ -module”. It is true thatRead more