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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 R

The 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.

SheafOfModules.free · cited by 60SheafOfModules.freeSheafOfModules.ιFree · cited by 15SheafOfModules.ιFreeSheafOfModules.mapFreeIso · cited by 12SheafOfModules.mapFreeIsoSheafOfModules.unitHomEquiv · cited by 6SheafOfModules.unitHomEqu…SheafOfModules.pullbackObjFreeIso · cited by 5SheafOfModules.pullbackOb…SheafOfModules.pullbackObjUnitToUnit · cited by 5SheafOfModules.pullbackOb…SheafOfModules.Presentation.map · cited by 5Presentation.mapSheafOfModules.GeneratingSections.map · cited by 4GeneratingSections.mapSheafOfModules.unitToPushforwardObjUnit · cited by 4SheafOfModules.unitToPush…SheafOfModules.freeFunctor · cited by 4SheafOfModules.freeFunctorSheafOfModules.Presentation.mapGenerators · cited by 4Presentation.mapGeneratorsSheafOfModules.Presentation.mapRelations · cited by 4Presentation.mapRelationsSheafOfModules.Presentation.quasicoherentData · cited by 4Presentation.quasicoheren…SheafOfModules.isColimitFreeCofan · cited by 4SheafOfModules.isColimitF…SheafOfModules.GeneratingSections.localGeneratorsData · cited by 3GeneratingSections.localG…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.ObjectProperty.FullSubcategory.obj · cited by 1316FullSubcategory.objCategoryTheory.Sheaf · cited by 763CategoryTheory.SheafRingCat · cited by 473RingCatSheafOfModules · cited by 188SheafOfModulesPresheafOfModules.unit · cited by 3PresheafOfModules.unitSheafOfModules.unitCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by71

Results whose statement or proof uses this declaration.