Theorems · Theorem · category theory

CategoryTheory.Limits.coequalizer.hom_ext

∀ {C : Type u} {X Y : C} [inst : CategoryTheory.Category.{v, u} C] {f g : X ⟶ Y}
  [inst_1 : CategoryTheory.Limits.HasCoequalizer f g] {W : C} {k l : CategoryTheory.Limits.coequalizer f g ⟶ W},
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coequalizer.π f g) k =
      CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coequalizer.π f g) l →
    k = l

Two maps from a coequalizer are equal if they are equal when composed with the coequalizer map

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Equalizers

Cited by

38 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoequalizer