Theorems · Definition · category theory
TopCat.Hom.frameHom
{X Y : TopCat} → (X ⟶ Y) → FrameHom (TopologicalSpace.Opens ↑Y) (TopologicalSpace.Opens ↑X)The FrameHom sending an open in Y to its preimage in X
- Defined in
- Mathlib.Topology.Category.TopCat.Opens
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- SetLike.coeproof · cited by 8,199
- Set.preimageproof · cited by 4,946
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- FrameHomstatement · cited by 70
Cited by4
Results whose statement or proof uses this declaration.
- TopologicalSpace.Opens.mapproof · cited by 645
- AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.to_isoproof · cited by 2
- AlgebraicGeometry.eq_zero_of_basicOpen_eq_botproof · cited by 1
- TopCat.Hom.coe_frameHom_toFunstatement and proof · cited by 0