Theorems · Theorem · category theory
Topology.IsOpenEmbedding.functor_obj_injective
∀ {X Y : TopCat} {f : X ⟶ Y} (hf : Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f)),
Function.Injective hf.functor.obj- Defined in
- Mathlib.Topology.Category.TopCat.Opens
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.Functor.objstatement and proof · cited by 19,642
- SetLike.coeproof · cited by 8,199
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsEmbedding.injectiveproof · cited by 103
- TopologicalSpace.Opens.extproof · cited by 83
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Opens.eq_presheaf_map_eqToHomstatement · cited by 0