Theorems · Definition · category theory

SheafOfModules.LocalGeneratorsData.quasiCoherentData

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R : CategoryTheory.Sheaf J RingCat} →
        [inst_1 : ∀ (X : C), CategoryTheory.HasSheafify (J.over X) AddCommGrpCat] →
          [inst_2 : ∀ (X : C), (J.over X).WEqualsLocallyBijective AddCommGrpCat] →
            {M : SheafOfModules R} → (q : M.LocalGeneratorsData) → [q.IsLocallyFreeData] → M.QuasicoherentData

Given locally free data, this is the QuasiCoherentData where there are no relations.

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.LocallyFree

Cited by

6 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijectiveSheafOfModules.LocalGeneratorsData.IsLocallyFreeData