Theorems · Definition · category theory

CategoryTheory.CommSq.shortComplex

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {X₁ X₂ X₃ X₄ : C} →
        [CategoryTheory.Limits.HasBinaryBiproduct X₂ X₃] →
          {f : X₁ ⟶ X₂} →
            {g : X₁ ⟶ X₃} →
              {inl : X₂ ⟶ X₄} → {inr : X₃ ⟶ X₄} → CategoryTheory.CommSq f g inl inr → CategoryTheory.ShortComplex C

The short complex attached to the cokernel cofork of a commutative square.

Defined in

Mathlib.Algebra.Homology.CommSq

Cited by

9 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproduct