Theorems · Definition · category theory
SheafOfModules.sections
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{J : CategoryTheory.GrothendieckTopology C} →
{R : CategoryTheory.Sheaf J RingCat} → SheafOfModules R → Type (max u₁ v)The type of sections of a sheaf of modules.
- Defined in
- Mathlib.Algebra.Category.ModuleCat.Sheaf
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 41 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.Sheafstatement and proof · cited by 763
- RingCatstatement and proof · cited by 473
- SheafOfModulesstatement and proof · cited by 188
- SheafOfModules.valproof · cited by 55
- PresheafOfModules.sectionsproof · cited by 7
Cited by42
Results whose statement or proof uses this declaration.
- SheafOfModules.freeHomEquivstatement and proof · cited by 20
- SheafOfModules.sectionsMapstatement and proof · cited by 12
- SheafOfModules.GeneratingSections.sstatement · cited by 10
- SheafOfModules.LocalGeneratorsData.quasiCoherentDataproof · cited by 6
- SheafOfModules.unitHomEquivstatement · cited by 6
- SheafOfModules.freeSectionstatement · cited by 5
- SheafOfModules.pushforwardSectionsstatement and proof · cited by 3
- SheafOfModules.ιFree_freeMapproof · cited by 3
- SheafOfModules.Presentation.isColimitstatement · cited by 2
- SheafOfModules.freeHomEquiv_freeMapstatement · cited by 2
- SheafOfModules.sectionsFunctorproof · cited by 2
- SheafOfModules.GeneratingSections.mk.injstatement and proof · cited by 1