Theorems · Definition · category theory
SheafOfModules.overFunctor
{D : Type u₂} →
[inst : CategoryTheory.Category.{v₂, u₂} D] →
{K : CategoryTheory.GrothendieckTopology D} →
(R : CategoryTheory.Sheaf K RingCat) →
(X : D) → CategoryTheory.Functor (SheafOfModules R) (SheafOfModules (R.over X))The restriction functor from sheaves of R-modules to sheaves of R.over X-modules
for some X : D.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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.
Cites11
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
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.Sheafstatement and proof · cited by 763
- RingCatstatement and proof · cited by 473
- SheafOfModulesstatement · cited by 188
- CategoryTheory.GrothendieckTopology.overstatement · cited by 115
- SheafOfModules.pushforwardproof · cited by 45
- CategoryTheory.Sheaf.overstatement and proof · cited by 26
Cited by5
Results whose statement or proof uses this declaration.
- SheafOfModules.overproof · cited by 15
- AlgebraicGeometry.Scheme.Modules.overFunctorEquivstatement · cited by 1
- AlgebraicGeometry.Scheme.Modules.exists_isOpenCover_presentationproof · cited by 1
- SheafOfModules.Hom.overproof · cited by 1
- SheafOfModules.overFunctorMapstatement and proof · cited by 0