Definition 101.15.2. Let f : \mathcal{X} \to \mathcal{Y} be a morphism of algebraic stacks. We say f is a universal homeomorphism if for every morphism of algebraic stacks \mathcal{Z} \to \mathcal{Y} the map of topological spaces
|\mathcal{Z} \times _\mathcal {Y} \mathcal{X}| \to |\mathcal{Z}|
is a homeomorphism.
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