Quotient space of an algebraic stack
In algebraic geometry, the quotient space of an algebraic stack F, denoted by |F|, is a topological space which as a set is the set of all integral substacks of F and which then is given a "Zariski topology": an open subset has a form for some open substack U of F.
The construction is functorial; i.e., each morphism of algebraic stacks determines a continuous map.
An algebraic stack X is punctual if is a point.
When X is a moduli stack, the quotient space is called the moduli space of X. If is a morphism of algebraic stacks that induces a homeomorphism, then Y is called a coarse moduli stack of X.
