Theorems · Definition · category theory

SheafOfModules.freeHomEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R : CategoryTheory.Sheaf J RingCat} →
        [inst_1 : CategoryTheory.HasWeakSheafify J AddCommGrpCat] →
          [inst_2 : J.WEqualsLocallyBijective AddCommGrpCat] →
            (M : SheafOfModules R) → {I : Type u} → (SheafOfModules.free I ⟶ M) ≃ (I → M.sections)

The data of a morphism free I ⟶ M from a free sheaf of modules is equivalent to the data of a family I → M.sections of sections of M.

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Free

Cited by

20 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective