Theorems · Definition · category theory
SheafOfModules.unit
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{J : CategoryTheory.GrothendieckTopology C} → (R : CategoryTheory.Sheaf J RingCat) → SheafOfModules RThe obvious free sheaf of modules of rank 1.
- Defined in
- Mathlib.Algebra.Category.ModuleCat.Sheaf
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 62 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.
Cites7
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.GrothendieckTopologystatement and proof · cited by 1,415
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- CategoryTheory.Sheafstatement and proof · cited by 763
- RingCatstatement and proof · cited by 473
- SheafOfModulesstatement · cited by 188
- PresheafOfModules.unitproof · cited by 3
Cited by71
Results whose statement or proof uses this declaration.
- SheafOfModules.freeproof · cited by 60
- SheafOfModules.ιFreestatement and proof · cited by 15
- SheafOfModules.mapFreeIsostatement and proof · cited by 12
- SheafOfModules.unitHomEquivstatement · cited by 6
- SheafOfModules.pullbackObjFreeIsoproof · cited by 5
- SheafOfModules.pullbackObjUnitToUnitstatement and proof · cited by 5
- SheafOfModules.Presentation.mapstatement and proof · cited by 5
- SheafOfModules.GeneratingSections.mapstatement and proof · cited by 4
- SheafOfModules.unitToPushforwardObjUnitstatement · cited by 4
- SheafOfModules.freeFunctorproof · cited by 4
- SheafOfModules.Presentation.mapGeneratorsstatement and proof · cited by 4
- SheafOfModules.Presentation.mapRelationsstatement and proof · cited by 4