Theorems · Theorem · category theory

TopCat.isInducing_prodMap

∀ {W X Y Z : TopCat} {f : W ⟶ X} {g : Y ⟶ Z},
  Topology.IsInducing ⇑(CategoryTheory.ConcreteCategory.hom f) →
    Topology.IsInducing ⇑(CategoryTheory.ConcreteCategory.hom g) →
      Topology.IsInducing ⇑(CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.prod.map f g))

Defined in: Mathlib.Topology.Category.TopCat.Limits.Products
Cited by: 1 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites23

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

DFunLike.coestatement and proof · cited by 62,936
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CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
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ContinuousMapstatement · cited by 2,491
CategoryTheory.Discretestatement · cited by 2,447
TopCatstatement and proof · cited by 1,889
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.pairstatement · cited by 536
CategoryTheory.Limits.prodstatement and proof · cited by 364

Cited by1

Results whose statement or proof uses this declaration.

TopCat.isEmbedding_prodMapproof · cited by 1