Theorems · Theorem · category theory

CategoryTheory.Limits.IsColimit.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.Cocone F} (h : CategoryTheory.Limits.IsColimit t) {W : C}
  {f f' : t.pt ⟶ W},
  (∀ (j : J), CategoryTheory.CategoryStruct.comp (t.ι.app j) f = CategoryTheory.CategoryStruct.comp (t.ι.app j) f') →
    f = f'

Two morphisms out of a colimit are equal if their compositions with each cocone morphism are equal.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

58 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category