Theorems · Theorem · category theory

CategoryTheory.Limits.Concrete.limit_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {FC : C → C → Type u_1} {CC : C → Type r}
  [inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC] {J : Type w}
  [inst_3 : CategoryTheory.Category.{t, w} J] (F : CategoryTheory.Functor J C)
  [CategoryTheory.Limits.PreservesLimit F (CategoryTheory.forget C)] [inst_5 : CategoryTheory.Limits.HasLimit F]
  (x y : CategoryTheory.ToType (CategoryTheory.Limits.limit F)),
  (∀ (j : J),
      (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.limit.π F j)) x =
        (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.limit.π F j)) y) →
    x = y

Defined in

Mathlib.CategoryTheory.Limits.ConcreteCategory.Basic

Cited by

6 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimitCategoryTheory.Limits.HasLimit