Theorems · Inductive type · category theory

CategoryTheory.ShortComplex.LeftHomologyMapData

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S₁ S₂ : CategoryTheory.ShortComplex C} → (S₁ ⟶ S₂) → S₁.LeftHomologyData → S₂.LeftHomologyData → Type v_1

Given left homology data h₁ and h₂ for two short complexes S₁ and S₂, a LeftHomologyMapData for a morphism φ : S₁ ⟶ S₂ consists of a description of the induced morphisms on the K (cycles) and H (left homology) fields of h₁ and h₂.

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

66 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms