Theorems · Theorem · category theory

CategoryTheory.Presieve.Arrows.PullbackCompatible.congr_simp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (P : CategoryTheory.Functor Cᵒᵖ (Type w)) {B : C}
  {I : Type u_1} {X : I → C} (π π_1 : (i : I) → X i ⟶ B) (e_π : π = π_1)
  [inst_1 : (CategoryTheory.Presieve.ofArrows X π).HasPairwisePullbacks] (x x_1 : (i : I) → P.obj (Opposite.op (X i))),
  x = x_1 →
    CategoryTheory.Presieve.Arrows.PullbackCompatible P π x =
      CategoryTheory.Presieve.Arrows.PullbackCompatible P π_1 x_1

Defined in

Mathlib.CategoryTheory.Sites.IsSheafFor

Cited by

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Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Presieve.HasPairwisePullbacks