Theorems · Theorem · category theory

CategoryTheory.Limits.Concrete.widePullback_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type (max v w)}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC] {B : C}
  {ι : Type w} {X : ι → C} (f : (j : ι) → X j ⟶ B) [inst_3 : CategoryTheory.Limits.HasWidePullback B X f]
  [CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.WidePullbackShape.wideCospan B X f)
      (CategoryTheory.forget C)]
  (x y : CategoryTheory.ToType (CategoryTheory.Limits.widePullback B X f)),
  (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.WidePullback.base f)) x =
      (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.WidePullback.base f)) y →
    (∀ (j : ι),
        (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.WidePullback.π f j)) x =
          (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.WidePullback.π f j)) y) →
      x = y

Defined in

Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.Limits.HasWidePullbackCategoryTheory.Limits.PreservesLimit