Theorems · Theorem · category theory

TopCat.fst_iso_of_right_embedding_range_subset

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

Defined in: Mathlib.Topology.Category.TopCat.Limits.Pullbacks
Cited by: 0 results in Mathlib
Foundations: Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

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