Theorems · Theorem · category theory

CategoryTheory.Limits.Concrete.multiequalizer_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type s}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC]
  {J : CategoryTheory.Limits.MulticospanShape} {I : CategoryTheory.Limits.MulticospanIndex J C}
  [inst_3 : CategoryTheory.Limits.HasMultiequalizer I]
  [CategoryTheory.Limits.PreservesLimit I.multicospan (CategoryTheory.forget C)]
  (x y : CategoryTheory.ToType (CategoryTheory.Limits.multiequalizer I)),
  (∀ (t : J.L),
      (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.Multiequalizer.ι I t)) x =
        (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.Multiequalizer.ι I t)) y) →
    x = y

Defined in

Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.Limits.HasMultiequalizerCategoryTheory.Limits.PreservesLimit