Theorems · Theorem · category theory
Topology.IsInducing.le_functorObj_iff
∀ {X Y : TopCat} {f : X ⟶ Y} (hf : Topology.IsInducing ⇑(CategoryTheory.ConcreteCategory.hom f))
{U : TopologicalSpace.Opens ↑X} {V : TopologicalSpace.Opens ↑Y},
V ≤ hf.functorObj U ↔ (TopologicalSpace.Opens.map f).obj V ≤ U- Defined in
- Mathlib.Topology.Category.TopCat.Opens
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites24
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
- Setproof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Set.preimageproof · cited by 4,946
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- IsOpenproof · cited by 2,400
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- TopologicalSpace.Opens.mapstatement and proof · cited by 645
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