Theorems · Theorem · category theory

TopCat.snd_isOpenEmbedding_of_left

∀ {X Y S : TopCat} {f : X ⟶ S},
  Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f) →
    ∀ (g : Y ⟶ S),
      Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.pullback.snd f g))

Defined in: Mathlib.Topology.Category.TopCat.Limits.Pullbacks
Cited by: 2 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites29

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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Cited by3

Results whose statement or proof uses this declaration.

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullbackConeOfLeftFststatement · cited by 1
TopCat.isOpenEmbedding_of_pullbackproof · cited by 0
AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_cone_of_left_conditionstatement and proof · cited by 0