Theorems · Theorem · category theory

CategoryTheory.Limits.colimit.hom_ext

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  {F : CategoryTheory.Functor J C} [inst_2 : CategoryTheory.Limits.HasColimit F] {X : C}
  {f f' : CategoryTheory.Limits.colimit F ⟶ X},
  (∀ (j : J),
      CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.colimit.ι F j) f =
        CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.colimit.ι F j) f') →
    f = f'

Defined in

Mathlib.CategoryTheory.Limits.HasLimits

Cited by

54 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimit