ScalingStacks

Let $A$ be a free graded $R$-module of rank $2$ spanned by $\mathbf{1}$ and $X$ with

$${\mathrm{deg}}(\mathbf{1})=1,\hskip 21.68121pt{\mathrm{deg}}(X)=-1$$

(11)

We equip $A$ with a commutative algebra structure with the unit $\mathbf{1}$ and multiplication

$$\mathbf{1}X=X\mathbf{1}=X,X^{2}=0.$$

(12)

We denote by $\iota$ the unit map $R\to A$ which sends $1$ to $\mathbf{1}.$ This map is a graded map of graded $R$-modules and it increases the degree by $1.$