Theorems · Definition · category theory

CategoryTheory.Sheaf.freeYonedaHomEquiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {A : Type u'} →
        [inst_1 : CategoryTheory.Category.{v', u'} A] →
          [inst_2 : CategoryTheory.Limits.HasCoproducts A] →
            [inst_3 : CategoryTheory.HasWeakSheafify J A] →
              {X : C} →
                {M : A} →
                  {F : CategoryTheory.Sheaf J A} →
                    (CategoryTheory.Sheaf.freeYoneda J X M ⟶ F) ≃ (M ⟶ F.obj.obj (Opposite.op X))

The bijection (Sheaf.freeYoneda J X M ⟶ F) ≃ (M ⟶ F.val.obj (op X)) when F : Sheaf J A, X : C and M : A.

Defined in

Mathlib.CategoryTheory.Generator.Sheaf

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.HasWeakSheafify