Theorems · Definition · category theory
TopologicalSpace.Opens.overEquivalence
{X : Type u} →
[inst : TopologicalSpace X] → (U : TopologicalSpace.Opens X) → CategoryTheory.Over U ≌ TopologicalSpace.Opens ↥UIf X is a topological space and U : Opens X,
then the category Over U is equivalent to Opens ↥U.
- Defined in
- Mathlib.Topology.Sheaves.Over
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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.
- Quiver.Homproof · cited by 32,603
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- CategoryTheory.Overstatement and proof · cited by 935
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.homOfLEproof · cited by 554
- CategoryTheory.Over.leftproof · cited by 541
- CategoryTheory.Over.mkproof · cited by 203
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
Cited by22
Results whose statement or proof uses this declaration.
- TopologicalSpace.Opens.sheafEquivOverproof · cited by 10
- AlgebraicGeometry.Scheme.Modules.overFunctorEquivproof · cited by 1
- TopologicalSpace.Opens.mem_overEquivalence_functor_objstatement · cited by 0
- TopologicalSpace.Opens.coe_overEquivalence_functor_objstatement and proof · cited by 0
- TopologicalSpace.Opens.coe_overEquivalence_inverse_obj_leftstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Modules.overMapCompOverEquivproof · cited by 0
- TopologicalSpace.Opens.overEquivalence_counitIso_hom_appstatement and proof · cited by 0
- TopologicalSpace.Opens.overEquivalence_counitIso_inv_appstatement and proof · cited by 0
- TopologicalSpace.Opens.overEquivalence_inverse_obj_right_asstatement and proof · cited by 0
- TopologicalSpace.Opens.overEquivalence_unitIso_hom_app_leftstatement and proof · cited by 0
- TopologicalSpace.Opens.overEquivalence_unitIso_inv_app_leftstatement and proof · cited by 0
- TopologicalSpace.Opens.sheafEquivOver_counitIso_hom_app_hom_appstatement · cited by 0