Theorems · Theorem · category theory

CategoryTheory.Meq.equiv_symm_eq_apply

∀ {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]
  [inst_4 :
    ∀ {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)] (x : CategoryTheory.Meq P S) (I : S.Arrow),
  (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.Multiequalizer.ι (S.index P) I))
      ((CategoryTheory.Meq.equiv P S).symm x) =
    ↑x I

Defined in

Mathlib.CategoryTheory.Sites.ConcreteSheafification

Cited by

4 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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