Theorems · Definition · algebraic geometry

SheafOfModules.QuasicoherentData.ofIsIso

{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 N : SheafOfModules R} →
              (f : M ⟶ N) → [CategoryTheory.IsIso f] → M.QuasicoherentData → N.QuasicoherentData

Mapping quasicoherent data under an isomorphism.

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent

Cited by

3 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijectiveCategoryTheory.IsIso