The Stacks project

94.3 Notation

We use the letters $S, T, U, V, X, Y$ to indicate schemes. We use the letters $\mathcal{X}, \mathcal{Y}, \mathcal{Z}$ to indicate categories (fibred, fibred in groupoids, stacks, ...) over $(\mathit{Sch}/S)_{fppf}$. We use small case letters $f$, $g$ for functors such as $f : \mathcal{X} \to \mathcal{Y}$ over $(\mathit{Sch}/S)_{fppf}$. We use capital $F$, $G$, $H$ for algebraic spaces over $S$, and more generally for presheaves of sets on $(\mathit{Sch}/S)_{fppf}$. (In future chapters we will revert to using also $X$, $Y$, etc for algebraic spaces.)

The reason for these choices is that we want to clearly distinguish between the different types of objects in this chapter, to build the foundations.