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The Stacks project

Definition 67.7.2. Let S be a scheme. Let f : X \to Y be a morphism of algebraic spaces over S.

  1. We say f is submersive1 if the continuous map |X| \to |Y| is submersive, see Topology, Definition 5.6.3.

  2. We say f is universally submersive if for every morphism of algebraic spaces Y' \to Y the base change Y' \times _ Y X \to Y' is submersive.

[1] This is very different from the notion of a submersion of differential manifolds.

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