Theorems · Theorem · category theory

CategoryTheory.NormalEpiCategory.hasColimit_parallelPair

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [CategoryTheory.Limits.HasFiniteCoproducts C] [CategoryTheory.Limits.HasCokernels C]
  [CategoryTheory.IsNormalEpiCategory C] {X Y : C} (f g : X ⟶ Y),
  CategoryTheory.Limits.HasColimit (CategoryTheory.Limits.parallelPair f g)

The coequalizer of f and g exists.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Equalizers

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasFiniteCoproductsCategoryTheory.Limits.HasCokernelsCategoryTheory.IsNormalEpiCategory