Theorems · Definition · category theory

CategoryTheory.Meq.equiv

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {D : Type w} →
        [inst_1 : CategoryTheory.Category.{w', w} D] →
          {FD : D → D → Type u_1} →
            {CD : D → Type t} →
              [inst_2 : (X Y : D) → FunLike (FD X Y) (CD X) (CD Y)] →
                [inst_3 : CategoryTheory.ConcreteCategory D FD] →
                  [∀ {X : C} (S : J.Cover X),
                        CategoryTheory.Limits.PreservesLimitsOfShape (CategoryTheory.Limits.WalkingMulticospan S.shape)
                          (CategoryTheory.forget D)] →
                    {X : C} →
                      (P : CategoryTheory.Functor Cᵒᵖ D) →
                        (S : J.Cover X) →
                          [inst_5 : CategoryTheory.Limits.HasMultiequalizer (S.index P)] →
                            CategoryTheory.ToType (CategoryTheory.Limits.multiequalizer (S.index P)) ≃
                              CategoryTheory.Meq P S

The equivalence between the type associated to multiequalizer (S.index P) and Meq P S.

Defined in

Mathlib.CategoryTheory.Sites.ConcreteSheafification

Cited by

8 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.Limits.PreservesLimitsOfShapeCategoryTheory.Limits.HasMultiequalizer