Theorems · Theorem · category theory

CategoryTheory.Equalizer.Presieve.Arrows.SecondObj.ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (P : CategoryTheory.Functor Cᵒᵖ (Type w)) {B : C} {I : Type t}
  [inst_1 : Small.{w, t} I] (X : I → C) (π : (i : I) → X i ⟶ B)
  [inst_2 : (CategoryTheory.Presieve.ofArrows X π).HasPairwisePullbacks]
  (z₁ z₂ : CategoryTheory.Equalizer.Presieve.Arrows.SecondObj P X π),
  (∀ (ij : I × I),
      (CategoryTheory.ConcreteCategory.hom
            (CategoryTheory.Limits.Pi.π
              (fun ij => P.obj (Opposite.op (CategoryTheory.Limits.pullback (π ij.1) (π ij.2)))) ij))
          z₁ =
        (CategoryTheory.ConcreteCategory.hom
            (CategoryTheory.Limits.Pi.π
              (fun ij => P.obj (Opposite.op (CategoryTheory.Limits.pullback (π ij.1) (π ij.2)))) ij))
          z₂) →
    z₁ = z₂

Defined in

Mathlib.CategoryTheory.Sites.EqualizerSheafCondition

Cited by

3 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategorySmallCategoryTheory.Presieve.HasPairwisePullbacks