Theorems · Inductive type · category theory

CategoryTheory.ShortComplex.LeftHomologyData

{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 left homology data for a short complex S consists of morphisms i : K ⟶ S.X₂ and π : K ⟶ H such that i identifies K to the kernel of g : S.X₂ ⟶ S.X₃, and that π identifies H to the cokernel of the induced map f' : S.X₁ ⟶ K

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

212 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms