Theorems · Theorem · category theory

CategoryTheory.ShortComplex.LeftHomologyData.liftCycles_comp_cyclesIso_hom

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S : CategoryTheory.ShortComplex C} (h : S.LeftHomologyData) {A : C} (k : A ⟶ S.X₂)
  (hk : CategoryTheory.CategoryStruct.comp k S.g = 0) [inst_2 : S.HasLeftHomology],
  CategoryTheory.CategoryStruct.comp (S.liftCycles k hk) h.cyclesIso.hom = h.liftK k hk

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

2 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomology