Theorems · Definition · algebraic geometry

SheafOfModules.QuasicoherentData.presentation

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R : CategoryTheory.Sheaf J RingCat} →
        [inst_1 : ∀ (X : C), CategoryTheory.HasWeakSheafify (J.over X) AddCommGrpCat] →
          [inst_2 : ∀ (X : C), (J.over X).WEqualsLocallyBijective AddCommGrpCat] →
            {M : SheafOfModules R} → (self : M.QuasicoherentData) → (i : self.I) → (M.over (self.X i)).Presentation

a presentation of the sheaf of modules M.over (X i) for any i : I

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent

Cited by

6 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective