Theorems · Definition · category theory

CategoryTheory.Functor.IsCoverDense.Types.sheafIso

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {K : CategoryTheory.GrothendieckTopology D} →
          {G : CategoryTheory.Functor C D} →
            [G.IsCoverDense K] →
              [G.IsLocallyFull K] →
                {ℱ ℱ' : CategoryTheory.Sheaf K (Type v)} → (G.op.comp ℱ.obj ≅ G.op.comp ℱ'.obj) → (ℱ ≅ ℱ')

Given a natural isomorphism G ⋙ ℱ ≅ G ⋙ ℱ' between presheaves of types, where G is locally-full and cover-dense, and ℱ, ℱ' are sheaves, we may obtain a natural isomorphism between sheaves.

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.Basic

Cited by

2 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsCoverDenseCategoryTheory.Functor.IsLocallyFull