Automatic right t-exactness of tensor products

Remark 8.5.12. By Observation 8.5.9, the functor \((-) \otimes _R N\) is automatically right t-exact when \(N\) is connective. Thus a connective left \(R\)-module \(N\) is flat if and only if this functor is left t-exact: for every coconnective right \(R\)-module \(M\), the spectrum \(M \otimes _R N\) is coconnective.