Theorems · Theorem · category theory

CompHausLike.finitaryExtensive

∀ {P : TopCat → Prop} [CompHausLike.HasExplicitFiniteCoproducts P],
  (∀ ⦃X Y B : CompHausLike P⦄ (f : X ⟶ B) (g : Y ⟶ B),
      Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f) → CompHausLike.HasExplicitPullback f g) →
    CategoryTheory.FinitaryExtensive (CompHausLike P)

Defined in: Mathlib.Topology.Category.CompHausLike.Limits
Cited by: 0 results in Mathlib
Foundations: Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CompHausLike.HasExplicitFiniteCoproducts

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Cites16

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
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement · cited by 3,184
ContinuousMapstatement · cited by 2,491
TopCatstatement and proof · cited by 1,889
CompHausLike.toTopstatement · cited by 258
Topology.IsOpenEmbeddingstatement and proof · cited by 231
CompHausLikestatement and proof · cited by 145
CategoryTheory.FinitaryExtensivestatement · cited by 38
CompHausLike.HasExplicitFiniteCoproductsstatement and proof · cited by 28
CompHausLike.HasExplicitPullbackstatement and proof · cited by 14

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