Theorems · Theorem · category theory

HomologicalComplex.opcyclesMap_comp_descOpcycles

∀ {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 : L.X i ⟶ A) (j : ι) (hj : c.prev i = j)
  (hk : CategoryTheory.CategoryStruct.comp (L.d j i) k = 0) (φ : K ⟶ L),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.opcyclesMap φ i) (L.descOpcycles k j hj hk) =
    K.descOpcycles (CategoryTheory.CategoryStruct.comp (φ.f i) k) j hj ⋯

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

2 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomologyHomologicalComplex.HasHomology