Theorems · Definition · category theory

CategoryTheory.kernelCokernelCompSequence

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.Abelian C] → {X Y Z : C} → (X ⟶ Y) → (Y ⟶ Z) → CategoryTheory.ComposableArrows C 5

If f : X ⟶ Y and g : Y ⟶ Z are composable morphisms in an abelian category, this is the long exact sequence 0 ⟶ ker f ⟶ ker (f ≫ g) ⟶ ker g ⟶ coker f ⟶ coker (f ≫ g) ⟶ coker g ⟶ 0.

Defined in

Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian