Theorems · Theorem · category theory

CategoryTheory.Limits.IsLimit.hom_ext

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} C]
  {F : CategoryTheory.Functor J C} {t : CategoryTheory.Limits.Cone F} (h : CategoryTheory.Limits.IsLimit t) {W : C}
  {f f' : W ⟶ t.pt},
  (∀ (j : J), CategoryTheory.CategoryStruct.comp f (t.π.app j) = CategoryTheory.CategoryStruct.comp f' (t.π.app j)) →
    f = f'

Two morphisms into a limit are equal if their compositions with each cone morphism are equal.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

43 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category