Theorems · Theorem · category theory
TopologicalSpace.Opens.functor_map_eq_inf
∀ {X : TopCat} (U V : TopologicalSpace.Opens ↑X),
⋯.functor.obj ((TopologicalSpace.Opens.map U.inclusion').obj V) = V ⊓ U- Defined in
- Mathlib.Topology.Category.TopCat.Opens
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- SetLike.coeproof · cited by 8,199
- 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
- TopologicalSpace.Opens.mapstatement and proof · cited by 645
- Set.image_congrproof · cited by 533
- Set.image_preimage_eq_inter_rangeproof · cited by 121
- TopologicalSpace.Opens.extproof · cited by 83
- TopologicalSpace.Opens.toTopCatstatement and proof · cited by 81
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isPullback_opens_infproof · cited by 1
- AlgebraicGeometry.isPullback_opens_inf_leproof · cited by 0
- AlgebraicGeometry.PresheafedSpace.ofRestrict_top_cproof · cited by 0