Theorems · Definition · category theory

SheafOfModules.LocalGeneratorsData.generators

{C : Type u'} →
  [inst : CategoryTheory.Category.{v', u'} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R : CategoryTheory.Sheaf J RingCat} →
        {M : SheafOfModules R} →
          [inst_1 : ∀ (X : C), CategoryTheory.HasWeakSheafify (J.over X) AddCommGrpCat] →
            [inst_2 : ∀ (X : C), (J.over X).WEqualsLocallyBijective AddCommGrpCat] →
              (self : M.LocalGeneratorsData) → (i : self.I) → (M.over (self.X i)).GeneratingSections

the data of sections of M over X i which generate M.over (X i)

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators

Cited by

6 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective