Theorems · Theorem · category theory

CategoryTheory.Meq.equiv.congr_simp

∀ {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)],
  CategoryTheory.Meq.equiv P S = CategoryTheory.Meq.equiv P S

Defined in

Mathlib.CategoryTheory.Sites.ConcreteSheafification

Cited by

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Foundations

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

Assumes

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