Theorems · Definition · category theory

CategoryTheory.ShortComplex.cyclesMapIso

{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) → [inst_2 : S₁.HasLeftHomology] → [inst_3 : S₂.HasLeftHomology] → S₁.cycles ≅ S₂.cycles

The isomorphism S₁.cycles ≅ S₂.cycles induced by an isomorphism of short complexes S₁ ≅ S₂.

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

4 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomologyCategoryTheory.ShortComplex.HasLeftHomology