Theorems · Definition · category theory
SheafOfModules.val
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{J : CategoryTheory.GrothendieckTopology C} →
{R : CategoryTheory.Sheaf J RingCat} → SheafOfModules R → PresheafOfModules R.objthe underlying presheaf of modules of a sheaf of modules
- Defined in
- Mathlib.Algebra.Category.ModuleCat.Sheaf
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 36 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.
Cites10
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
- PresheafOfModulesstatement · cited by 247
- SheafOfModulesstatement and proof · cited by 188
Cited by78
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Modules.presheafproof · cited by 59
- SheafOfModules.pushforwardproof · cited by 45
- SheafOfModules.Hom.valstatement · cited by 39
- SheafOfModules.sectionsproof · cited by 28
- SheafOfModules.forgetproof · cited by 10
- SheafOfModules.pushforwardCongrproof · cited by 9
- AlgebraicGeometry.Scheme.Modules.smulproof · cited by 9
- SheafOfModules.pushforwardNatTransproof · cited by 8
- SheafOfModules.hom_extstatement · cited by 7
- SheafOfModules.toSheafproof · cited by 6
- SheafOfModules.unitHomEquivproof · cited by 6
- AlgebraicGeometry.Scheme.Modules.hom_extproof · cited by 3