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 | U | ⊂ | F | {\displaystyle |U|\subset |F|} for some open substack U of F. The construction X ↦ | X | {\displaystyle X\mapsto |X|} is functorial; i.e., each morphism f : X → Y {\displaystyle f:X\to Y} of algebraic stacks determines a continuous map f : | X | → | Y | {\displaystyle f:|X|\to |Y|} . An algebraic stack X is punctual if | X | {\displaystyle |X|} is a point.

Source: Wikipedia — Quotient space of an algebraic stack (CC BY-SA 4.0)

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 | U | ⊂ | F | {\displaystyle |U|\subset |F|} for some open substack U of F. The construction X ↦ | X | {\displaystyle X\mapsto |X|} is functorial; i.e., each morphism f : X → Y {\displaystyle f:X\to Y} of algebraic stacks determines a continuous map f : | X | → | Y | {\displaystyle f:|X|\to |Y|} . An algebraic stack X is punctual if | X | {\displaystyle |X|} is a point.

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Source: Wikipedia "Quotient space of an algebraic stack" · CC BY-SA 4.0

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