Theorems · Theorem · category theory

TopCat.snd_iso_of_left_embedding_range_subset

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

Defined in: Mathlib.Topology.Category.TopCat.Limits.Pullbacks
Cited by: 1 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

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

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Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Iso.homproof · cited by 7,684
Set.Elemproof · cited by 7,166
Set.rangestatement and proof · cited by 4,705
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TopCat.carrierstatement and proof · cited by 3,184
ContinuousMapstatement · cited by 2,491
TopCatstatement and proof · cited by 1,889
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.pullback_snd_isIso_of_range_subsetproof · cited by 0