Theorems · Definition · category theory
SheafOfModules.fullyFaithfulForget
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{J : CategoryTheory.GrothendieckTopology C} →
(R : CategoryTheory.Sheaf J RingCat) → (SheafOfModules.forget R).FullyFaithfulThe forget functor SheafOfModules R ⥤ PresheafOfModules R.val is fully faithful.
- Defined in
- Mathlib.Algebra.Category.ModuleCat.Sheaf
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 45 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.
Cites14
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.Functor.objproof · cited by 19,642
- 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 by8
Results whose statement or proof uses this declaration.
- SheafOfModules.pushforwardCongrproof · cited by 9
- SheafOfModules.unitHomEquivproof · cited by 6
- AlgebraicGeometry.Scheme.Modules.restrictUnitIsoproof · cited by 1
- SheafOfModules.overFunctorMapproof · cited by 0
- SheafOfModules.PullbackConstruction.adjunctionproof · cited by 0
- PresheafOfModules.sheafifyHomEquivproof · cited by 0
- AlgebraicGeometry.Scheme.Modules.fullyFaithfulToPresheafOfModulesproof · cited by 0
- SheafOfModules.fullyFaithfulForget_preimage_valstatement and proof · cited by 0