Theorems · Theorem · category theory

CategoryTheory.Presieve.FamilyOfElements.sieveExtend.congr_simp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : C}
  {R : CategoryTheory.Presieve X} (x x_1 : CategoryTheory.Presieve.FamilyOfElements P R),
  x = x_1 →
    ∀ ⦃Y : C⦄ (f f_1 : Y ⟶ X) (e_f : f = f_1) (a : (CategoryTheory.Sieve.generate R).arrows f),
      x.sieveExtend f a = x_1.sieveExtend f_1 ⋯

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

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Foundations

Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category