Theorems · Definition · category theory

SheafOfModules.GeneratingSections.s

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

a family of sections which generate the sheaf of modules

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators

Cited by

10 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective