Theorems · Definition · category theory

CategoryTheory.kernelCokernelCompSequence.snakeInput

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] → {X Y Z : C} → (X ⟶ Y) → (Y ⟶ Z) → CategoryTheory.ShortComplex.SnakeInput C

The "snake input" which gives the exact sequence 0 ⟶ ker f ⟶ ker (f ≫ g) ⟶ ker g ⟶ coker f ⟶ coker (f ≫ g) ⟶ coker g ⟶ 0, see kernelCokernelCompSequence_exact.

Defined in

Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp

Cited by

31 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian