Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyMapData.ofEpiOfIsIsoOfMono

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S₁ S₂ : CategoryTheory.ShortComplex C} →
        (φ : S₁ ⟶ S₂) →
          (h : S₁.LeftHomologyData) →
            [inst_2 : CategoryTheory.Epi φ.τ₁] →
              [inst_3 : CategoryTheory.IsIso φ.τ₂] →
                [inst_4 : CategoryTheory.Mono φ.τ₃] →
                  CategoryTheory.ShortComplex.LeftHomologyMapData φ h
                    (CategoryTheory.ShortComplex.LeftHomologyData.ofEpiOfIsIsoOfMono φ h)

This left homology map data expresses compatibilities of the left homology data constructed by LeftHomologyData.ofEpiOfIsIsoOfMono

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

3 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.EpiCategoryTheory.IsIsoCategoryTheory.Mono