Theorems · Theorem · category theory

HomologicalComplex.singleObjCyclesSelfIso_hom_naturality

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] {ι : Type u_1} [inst_3 : DecidableEq ι] (c : ComplexShape ι) (j : ι)
  {A B : C} (f : A ⟶ B),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.cyclesMap ((HomologicalComplex.single C c j).map f) j)
      (HomologicalComplex.singleObjCyclesSelfIso c j B).hom =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.singleObjCyclesSelfIso c j A).hom f

Defined in

Mathlib.Algebra.Homology.SingleHomology

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq