Theorems · Theorem · category theory

CategoryTheory.ShortComplex.LeftHomologyData.lift_K_comp_cyclesIso_inv_assoc

∀ {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] {Z : C} (h_1 : S.cycles ⟶ Z),
  CategoryTheory.CategoryStruct.comp (h.liftK k hk) (CategoryTheory.CategoryStruct.comp h.cyclesIso.inv h_1) =
    CategoryTheory.CategoryStruct.comp (S.liftCycles k hk) h_1

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomology