Theorems · Definition · category theory

CategoryTheory.IsPushout.isColimitCokernelCofork

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {X₁ X₂ X₃ X₄ : C} →
        [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X₂ X₃] →
          {f : X₁ ⟶ X₂} →
            {g : X₁ ⟶ X₃} →
              {inl : X₂ ⟶ X₄} →
                {inr : X₃ ⟶ X₄} →
                  (h : CategoryTheory.IsPushout f g inl inr) → CategoryTheory.Limits.IsColimit ⋯.cokernelCofork

The colimit cokernel cofork attached to a pushout square.

Defined in

Mathlib.Algebra.Homology.CommSq

Cited by

3 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproduct