Theorems · Definition · category theory
TopCat.Presheaf.pullback
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[CategoryTheory.Limits.HasColimits C] →
{X Y : TopCat} → (X ⟶ Y) → CategoryTheory.Functor (TopCat.Presheaf C Y) (TopCat.Presheaf C X)Pullback a presheaf on Y along a continuous map f : X ⟶ Y, obtaining a presheaf
on X.
- Defined in
- Mathlib.Topology.Sheaves.Presheaf
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- TopCatstatement and proof · cited by 1,889
- CategoryTheory.Functor.opproof · cited by 997
- TopologicalSpace.Opens.mapproof · cited by 645
- TopCat.Presheafstatement · cited by 371
- CategoryTheory.Limits.HasColimitsstatement and proof · cited by 139
- CategoryTheory.Functor.lanproof · cited by 22
Cited by31
Results whose statement or proof uses this declaration.
- TopCat.Presheaf.germToPullbackStalkstatement · cited by 9
- TopCat.Presheaf.pullbackPushforwardAdjunctionstatement · cited by 9
- TopCat.Presheaf.pullbackObjObjOfImageOpenstatement · cited by 5
- TopCat.Presheaf.stalkPullbackHomstatement and proof · cited by 4
- IsOpenMap.pullbackObjIsostatement · cited by 3
- TopCat.Presheaf.stalkPullbackInvstatement and proof · cited by 2
- TopCat.Presheaf.germ_stalkPullbackHomstatement and proof · cited by 2
- TopCat.Presheaf.pullbackPushforwardAdjunction_unit_pullback_map_germToPullbackStalkstatement and proof · cited by 2
- TopCat.Presheaf.pullback_obj_obj_extstatement and proof · cited by 2
- IsOpenMap.pullbackIsostatement · cited by 2
- TopCat.Presheaf.germToPullbackStalk_stalkPullbackHomstatement and proof · cited by 1
- TopCat.Presheaf.germ_stalkPullbackInvstatement · cited by 1