Theorems · Theorem · category theory

HomologicalComplex.liftCycles_comp_cyclesMap_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {ι : Type u_2} {c : ComplexShape ι} {K L : HomologicalComplex C c} {i : ι} [inst_2 : K.HasHomology i]
  [inst_3 : L.HasHomology i] {A : C} (k : A ⟶ K.X i) (j : ι) (hj : c.next i = j)
  (hk : CategoryTheory.CategoryStruct.comp k (K.d i j) = 0) (φ : K ⟶ L) {Z : C} (h : L.cycles i ⟶ Z),
  CategoryTheory.CategoryStruct.comp (K.liftCycles k j hj hk)
      (CategoryTheory.CategoryStruct.comp (HomologicalComplex.cyclesMap φ i) h) =
    CategoryTheory.CategoryStruct.comp (L.liftCycles (CategoryTheory.CategoryStruct.comp k (φ.f i)) j hj ⋯) h

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomologyHomologicalComplex.HasHomology