Theorems · Definition · category theory

SheafOfModules.free.generatingSections

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R : CategoryTheory.Sheaf J RingCat} →
        [inst_1 : CategoryTheory.HasWeakSheafify J AddCommGrpCat] →
          [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat] → (I : Type u) → (SheafOfModules.free I).GeneratingSections

The generating sections of the free sheaf of modules.

Defined in: Mathlib.Algebra.Category.ModuleCat.Sheaf.LocallyFree
Cited by: 3 results in Mathlib
Foundations: Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.HasWeakSheafify CategoryTheory.GrothendieckTopology.WEqualsLocallyBijective

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Cites12

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
AddMonoidHomstatement · cited by 3,230
CategoryTheory.GrothendieckTopologystatement and proof · cited by 1,415
CategoryTheory.Sheafstatement and proof · cited by 763
RingCatstatement and proof · cited by 473
AddCommGrpCatstatement and proof · cited by 462
AddCommGrpCat.carrierstatement · cited by 407
CategoryTheory.HasWeakSheafifystatement and proof · cited by 221
CategoryTheory.GrothendieckTopology.WEqualsLocallyBijectivestatement and proof · cited by 142
SheafOfModules.freestatement · cited by 60
SheafOfModules.GeneratingSectionsstatement · cited by 27
SheafOfModules.freeSectionproof · cited by 5

Cited by3

Results whose statement or proof uses this declaration.

SheafOfModules.free.generatingSections_Istatement and proof · cited by 0
SheafOfModules.free.generatingSections_sstatement and proof · cited by 0
SheafOfModules.free.generatingSections_πstatement · cited by 0