Theorems · Theorem · category theory
SheafOfModules.isSheaf
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C}
{R : CategoryTheory.Sheaf J RingCat} (self : SheafOfModules R), CategoryTheory.Presheaf.IsSheaf J self.val.presheaf- Defined in
- Mathlib.Algebra.Category.ModuleCat.Sheaf
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Functorstatement · cited by 16,252
- Oppositestatement · cited by 8,081
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- CategoryTheory.Presheaf.IsSheafstatement · cited by 991
- CategoryTheory.Sheafstatement and proof · cited by 763
- RingCatstatement and proof · cited by 473
- Abstatement · cited by 198
- SheafOfModulesstatement and proof · cited by 188
- PresheafOfModules.presheafstatement · cited by 85
- SheafOfModules.valstatement · cited by 55
Cited by6
Results whose statement or proof uses this declaration.
- SheafOfModules.toSheafproof · cited by 6
- SheafOfModules.restrictScalarsproof · cited by 2
- SheafOfModules.toSheaf_map_homstatement · cited by 0
- AlgebraicGeometry.Scheme.Modules.isSheafproof · cited by 0
- SheafOfModules.restrictScalars_map_valstatement · cited by 0
- PresheafOfModules.sheafifyHomEquivproof · cited by 0