Theorems · Definition · category theory
TopologicalSpace.Opens.map
{X Y : TopCat} → (X ⟶ Y) → CategoryTheory.Functor (TopologicalSpace.Opens ↑Y) (TopologicalSpace.Opens ↑X)Opens.map f gives the functor from open sets in Y to open set in X,
given by taking preimages under f.
- Defined in
- Mathlib.Topology.Category.TopCat.Opens
- Cited by
- 645 results in Mathlib
- Foundations
- Depth 74 from the axioms, rests on 844 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- TopCat.carrierstatement · cited by 3,184
- TopologicalSpace.Opensstatement · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- OrderHomClass.toOrderHomproof · cited by 44
- OrderHom.toFunctorproof · cited by 4
- TopCat.Hom.frameHomproof · cited by 3
Cited by742
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.appstatement · cited by 176
- TopCat.Presheaf.pushforwardproof · cited by 174
- AlgebraicGeometry.Scheme.Hom.appLEstatement and proof · cited by 138
- AlgebraicGeometry.morphismRestrictstatement · cited by 90
- AlgebraicGeometry.Scheme.Hom.resLEstatement and proof · cited by 45
- AlgebraicGeometry.Scheme.Hom.preimage_image_eqstatement · cited by 37
- AlgebraicGeometry.Scheme.Hom.app_eq_appLEstatement and proof · cited by 32
- AlgebraicGeometry.Scheme.Hom.toNormalizationproof · cited by 28
- AlgebraicGeometry.Scheme.Hom.appLE_mapstatement and proof · cited by 27
- AlgebraicGeometry.morphismRestrict_ιstatement and proof · cited by 25
- AlgebraicGeometry.Scheme.Hom.map_appLEstatement and proof · cited by 24
- AlgebraicGeometry.image_morphismRestrict_preimagestatement · cited by 20
Showing the 200 most cited of 742.