Theorems · Inductive type · category theory

CategoryTheory.ShortComplex.RightHomologyData

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] → CategoryTheory.ShortComplex C → Type (max u_1 v_1)

A right homology data for a short complex S consists of morphisms p : S.X₂ ⟶ Q and ι : H ⟶ Q such that p identifies Q with the cokernel of f : S.X₁ ⟶ S.X₂, and that ι identifies H with the kernel of the induced map g' : Q ⟶ S.X₃

Defined in

Mathlib.Algebra.Homology.ShortComplex.RightHomology

Cited by

211 results in Mathlib

Foundations

Depth 3 from the axioms, rests on 4 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms