ScalingStacks

Definition 4.5.1.

A discrete \(Z\)-graded \(k\)-module \(M\) is flat if \(\oplus_{z \in Z} M_z\) is flat¹⁹ as a \(k\)-module. We let \(\mathrm{mod}_k^{Z, \mathrm{flat}}\) denote the full subcategory of the ordinary category of discrete \(Z\)-graded \(k\)-modules \(\mathrm{mod}_{k}^Z\) on the flat modules. A (not necessarily commutative) discrete \(Z\)-graded \(k\)-algebra \(A\) is flat if it is flat as a \(Z\)-graded \(k\)-module.