Theorems · Definition · category theory
CategoryTheory.Sheaf
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
CategoryTheory.GrothendieckTopology C →
(A : Type u₂) → [CategoryTheory.Category.{v₂, u₂} A] → Type (max (max (max u₂ v₂) u₁) v₁)The category of sheaves taking values in A on a Grothendieck topology.
- Defined in
- Mathlib.CategoryTheory.Sites.Sheaf
- Cited by
- 763 results in Mathlib
- Foundations
- Depth 34 from the axioms, rests on 311 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Presheaf.IsSheafproof · cited by 991
- CategoryTheory.ObjectProperty.FullSubcategoryproof · cited by 726
Cited by1,210
Results whose statement or proof uses this declaration.
- SheafOfModulesstatement · cited by 188
- CategoryTheory.sheafToPresheafstatement · cited by 142
- CategoryTheory.Functor.sheafPushforwardContinuousstatement · cited by 102
- TopCat.Sheafproof · cited by 73
- SheafOfModules.freestatement and proof · cited by 60
- CategoryTheory.presheafToSheafstatement · cited by 57
- SheafOfModules.valstatement and proof · cited by 55
- SheafOfModules.pushforwardstatement and proof · cited by 45
- SheafOfModules.unitstatement and proof · cited by 45
- SheafOfModules.Hom.valstatement and proof · cited by 39
- CategoryTheory.GrothendieckTopology.yonedastatement · cited by 37
- CategoryTheory.constantSheafstatement · cited by 30
Showing the 200 most cited of 1,210.