ScalingStacks

Observation 4.5.3.

An ordinary \(Z\)-graded \(k\)-module \(M\) is flat if and only if it is degreewise flat, i.e. each graded component \(M_z\) is a flat \(k\)-module for all \(z\in Z\). This follows from the fact that flatness is preserved under infinite coproducts and retracts.