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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.

SheafOfModules.freeHomEquiv · cited by 20SheafOfModules.freeHomEqu…SheafOfModules.sectionsMap · cited by 12SheafOfModules.sectionsMapSheafOfModules.GeneratingSections.s · cited by 10GeneratingSections.sSheafOfModules.LocalGeneratorsData.quasiCoherentData · cited by 6LocalGeneratorsData.quasi…SheafOfModules.unitHomEquiv · cited by 6SheafOfModules.unitHomEqu…SheafOfModules.freeSection · cited by 5SheafOfModules.freeSectionSheafOfModules.pushforwardSections · cited by 3SheafOfModules.pushforwar…SheafOfModules.ιFree_freeMap · cited by 3SheafOfModules.ιFree_free…SheafOfModules.Presentation.isColimit · cited by 2Presentation.isColimitSheafOfModules.freeHomEquiv_freeMap · cited by 2SheafOfModules.freeHomEqu…SheafOfModules.sectionsFunctor · cited by 2SheafOfModules.sectionsFu…SheafOfModules.GeneratingSections.mk.inj · cited by 1mk.injSheafOfModules.GeneratingSections.mk.noConfusion · cited by 1mk.noConfusionSheafOfModules.freeHomEquiv_symm_comp · cited by 1SheafOfModules.freeHomEqu…SheafOfModules.pushforwardSections_coe · cited by 1SheafOfModules.pushforwar…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.Sheaf · cited by 763CategoryTheory.SheafRingCat · cited by 473RingCatSheafOfModules · cited by 188SheafOfModulesSheafOfModules.val · cited by 55SheafOfModules.valPresheafOfModules.sections · cited by 7PresheafOfModules.sectionsSheafOfModules.sectionsCITED BYCITES

Cites7

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Cited by42

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