Theorems · Theorem · category theory

HomologicalComplex.descOpcycles_comp_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 : HomologicalComplex C c) {i : ι} [inst_2 : K.HasHomology i] {A A' : C}
  (k : K.X i ⟶ A) (j : ι) (hj : c.prev i = j) (hk : CategoryTheory.CategoryStruct.comp (K.d j i) k = 0) (α : A ⟶ A')
  {Z : C} (h : A' ⟶ Z),
  CategoryTheory.CategoryStruct.comp (K.descOpcycles k j hj hk) (CategoryTheory.CategoryStruct.comp α h) =
    CategoryTheory.CategoryStruct.comp (K.descOpcycles (CategoryTheory.CategoryStruct.comp k α) j hj ⋯) h

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomology