Theorems · Theorem · category theory
TopCat.IsInducing.empty
∀ (X : TopCat), Topology.IsInducing ⇑(CategoryTheory.ConcreteCategory.hom (TopCat.isInitialPEmpty.to X))
The unique map ∅ ⟶ X is inducing.
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- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setproof · cited by 53,352
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- TopCatstatement and proof · cited by 1,889
- Topology.IsInducingstatement · cited by 266
- CategoryTheory.Limits.IsInitial.tostatement · cited by 119
- TopologicalSpace.extproof · cited by 15
- TopCat.isInitialPEmptystatement · cited by 2
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