Theorems · Definition · category theory
SheafOfModules.forget
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{J : CategoryTheory.GrothendieckTopology C} →
(R : CategoryTheory.Sheaf J RingCat) → CategoryTheory.Functor (SheafOfModules R) (PresheafOfModules R.obj)The forgetful functor SheafOfModules.{v} R ⥤ PresheafOfModules R.val.
- Defined in
- Mathlib.Algebra.Category.ModuleCat.Sheaf
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 43 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.
Cites13
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.Homproof · cited by 32,603
- 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
- SheafOfModules.valproof · cited by 55
Cited by22
Results whose statement or proof uses this declaration.
- SheafOfModules.evaluationproof · cited by 11
- SheafOfModules.toSheafproof · cited by 6
- PresheafOfModules.sheafificationHomEquivstatement · cited by 4
- PresheafOfModules.sheafificationAdjunctionstatement and proof · cited by 3
- PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_defstatement · cited by 1
- PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symmstatement and proof · cited by 1
- SheafOfModules.fullyFaithfulForgetstatement and proof · cited by 1
- SheafOfModules.overFunctorMapproof · cited by 0
- SheafOfModules.PullbackConstruction.adjunctionstatement and proof · cited by 0
- PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_appstatement · cited by 0
- PresheafOfModules.toPresheaf_map_sheafificationHomEquivstatement and proof · cited by 0
- SheafOfModules.pullbackIsostatement · cited by 0