Theorems · Inductive type · algebraic geometry

SheafOfModules.QuasicoherentData

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R : CategoryTheory.Sheaf J RingCat} →
        [∀ (X : C), CategoryTheory.HasWeakSheafify (J.over X) AddCommGrpCat] →
          [∀ (X : C), (J.over X).WEqualsLocallyBijective AddCommGrpCat] →
            SheafOfModules R → Type (max (max (max (u + 1) u₁) v₁) (w + 1))

This structure contains the data of a family of objects X i which cover the terminal object, and of a presentation of M.over (X i) for all i.

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent

Cited by

16 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective